risk management research hypothesis

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• Published: 08 April 2024

A case study on the relationship between risk assessment of scientific research projects and related factors under the Naive Bayesian algorithm

• Xuying Dong 1 &
• Wanlin Qiu 1  

Scientific Reports volume  14 , Article number:  8244 ( 2024 ) Cite this article

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• Computer science
• Mathematics and computing

This paper delves into the nuanced dynamics influencing the outcomes of risk assessment (RA) in scientific research projects (SRPs), employing the Naive Bayes algorithm. The methodology involves the selection of diverse SRPs cases, gathering data encompassing project scale, budget investment, team experience, and other pertinent factors. The paper advances the application of the Naive Bayes algorithm by introducing enhancements, specifically integrating the Tree-augmented Naive Bayes (TANB) model. This augmentation serves to estimate risk probabilities for different research projects, shedding light on the intricate interplay and contributions of various factors to the RA process. The findings underscore the efficacy of the TANB algorithm, demonstrating commendable accuracy (average accuracy 89.2%) in RA for SRPs. Notably, budget investment (regression coefficient: 0.68, P < 0.05) and team experience (regression coefficient: 0.51, P < 0.05) emerge as significant determinants obviously influencing RA outcomes. Conversely, the impact of project size (regression coefficient: 0.31, P < 0.05) is relatively modest. This paper furnishes a concrete reference framework for project managers, facilitating informed decision-making in SRPs. By comprehensively analyzing the influence of various factors on RA, the paper not only contributes empirical insights to project decision-making but also elucidates the intricate relationships between different factors. The research advocates for heightened attention to budget investment and team experience when formulating risk management strategies. This strategic focus is posited to enhance the precision of RAs and the scientific foundation of decision-making processes.

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Introduction

Scientific research projects (SRPs) stand as pivotal drivers of technological advancement and societal progress in the contemporary landscape 1 , 2 , 3 . The dynamism of SRP success hinges on a multitude of internal and external factors 4 . Central to effective project management, Risk assessment (RA) in SRPs plays a critical role in identifying and quantifying potential risks. This process not only aids project managers in formulating strategic decision-making approaches but also enhances the overall success rate and benefits of projects. In a recent contribution, Salahuddin 5 provides essential numerical techniques indispensable for conducting RAs in SRPs. Building on this foundation, Awais and Salahuddin 6 delve into the assessment of risk factors within SRPs, notably introducing the consideration of activation energy through an exploration of the radioactive magnetohydrodynamic model. Further expanding the scope, Awais and Salahuddin 7 undertake a study on the natural convection of coupled stress fluids. However, RA of SRPs confronts a myriad of challenges, underscoring the critical need for novel methodologies 8 . Primarily, the intricate nature of SRPs renders precise RA exceptionally complex and challenging. The project’s multifaceted dimensions, encompassing technology, resources, and personnel, are intricately interwoven, posing a formidable challenge for traditional assessment methods to comprehensively capture all potential risks 9 . Furthermore, the intricate and diverse interdependencies among various project factors contribute to the complexity of these relationships, thereby limiting the efficacy of conventional methods 10 , 11 , 12 . Traditional approaches often focus solely on the individual impact of diverse factors, overlooking the nuanced relationships that exist between them—an inherent limitation in the realm of RA for SRPs 13 , 14 , 15 .

The pursuit of a methodology capable of effectively assessing project risks while elucidating the intricate interplay of different factors has emerged as a focal point in SRPs management 16 , 17 , 18 . This approach necessitates a holistic consideration of multiple factors, their quantification in contributing to project risks, and the revelation of their correlations. Such an approach enables project managers to more precisely predict and respond to risks. Marx-Stoelting et al. 19 , current approaches for the assessment of environmental and human health risks due to exposure to chemical substances have served their purpose reasonably well. Additionally, Awais et al. 20 highlights the significance of enthalpy changes in SRPs risk considerations, while Awais et al. 21 delve into the comprehensive exploration of risk factors in Eyring-Powell fluid flow in magnetohydrodynamics, particularly addressing viscous dissipation and activation energy effects. The Naive Bayesian algorithm, recognized for its prowess in probability and statistics, has yielded substantial results in information retrieval and data mining in recent years 22 . Leveraging its advantages in classification and probability estimation, the algorithm presents a novel approach for RA of SRPs 23 . Integrating probability analysis into RA enables a more precise estimation of project risks by utilizing existing project data and harnessing the capabilities of the Naive Bayesian algorithms. This method facilitates a quantitative, statistical analysis of various factors, effectively navigating the intricate relationships between them, thereby enhancing the comprehensiveness and accuracy of RA for SRPs.

This paper seeks to employ the Naive Bayesian algorithm to estimate the probability of risks by carefully selecting distinct research project cases and analyzing multidimensional data, encompassing project scale, budget investment, and team experience. Concurrently, Multiple Linear Regression (MLR) analysis is applied to quantify the influence of these factors on the assessment results. The paper places particular emphasis on exploring the intricate interrelationships between different factors, aiming to provide a more specific and accurate reference framework for decision-making in SRPs management.

This paper introduces several innovations and contributions to the field of RA for SRPs:

Comprehensive Consideration of Key Factors: Unlike traditional research that focuses on a single factor, this paper comprehensively considers multiple key factors, such as project size, budget investment, and team experience. This holistic analysis enhances the realism and thoroughness of RA for SRPs.

Introduction of Tree-Enhanced Naive Bayes Model: The naive Bayes algorithm is introduced and further improved through the proposal of a tree-enhanced naive Bayes model. This algorithm exhibits unique advantages in handling uncertainty and complexity, thereby enhancing its applicability and accuracy in the RA of scientific and technological projects.

Empirical Validation: The effectiveness of the proposed method is not only discussed theoretically but also validated through empirical cases. The analysis of actual cases provides practical support and verification, enhancing the credibility of the research results.

Application of MLR Analysis: The paper employs MLR analysis to delve into the impact of various factors on RA. This quantitative analysis method adds specificity and operability to the research, offering a practical decision-making basis for scientific and technological project management.

Discovery of New Connections and Interactions: The paper uncovers novel connections and interactions, such as the compensatory role of team experience for budget-related risks and the impact of the interaction between project size and budget investment on RA results. These insights provide new perspectives for decision-making in technology projects, contributing significantly to the field of RA for SRPs in terms of both importance and practical value.

The paper is structured as follows: “ Introduction ” briefly outlines the significance of RA for SRPs. Existing challenges within current research are addressed, and the paper’s core objectives are elucidated. A distinct emphasis is placed on the innovative aspects of this research compared to similar studies. The organizational structure of the paper is succinctly introduced, providing a brief overview of each section’s content. “ Literature review ” provides a comprehensive review of relevant theories and methodologies in the domain of RA for SRPs. The current research landscape is systematically examined, highlighting the existing status and potential gaps. Shortcomings in previous research are analyzed, laying the groundwork for the paper’s motivation and unique contributions. “ Research methodology ” delves into the detailed methodologies employed in the paper, encompassing data collection, screening criteria, preprocessing steps, and more. The tree-enhanced naive Bayes model is introduced, elucidating specific steps and the purpose behind MLR analysis. “ Results and discussion ” unfolds the results and discussions based on selected empirical cases. The representativeness and diversity of these cases are expounded upon. An in-depth analysis of each factor’s impact and interaction in the context of RA is presented, offering valuable insights. “ Discussion ” succinctly summarizes the entire research endeavor. Potential directions for further research and suggestions for improvement are proposed, providing a thoughtful conclusion to the paper.

Literature review

A review of ra for srps.

In recent years, the advancement of SRPs management has led to the evolution of various RA methods tailored for SRPs. The escalating complexity of these projects poses a challenge for traditional methods, often falling short in comprehensively considering the intricate interplay among multiple factors and yielding incomplete assessment outcomes. Scholars, recognizing the pivotal role of factors such as project scale, budget investment, and team experience in influencing project risks, have endeavored to explore these dynamics from diverse perspectives. Siyal et al. 24 pioneered the development and testing of a model geared towards detecting SRPs risks. Chen et al. 25 underscored the significance of visual management in SRPs risk management, emphasizing its importance in understanding and mitigating project risks. Zhao et al. 26 introduced a classic approach based on cumulative prospect theory, offering an optional method to elucidate researchers’ psychological behaviors. Their study demonstrated the enhanced rationality achieved by utilizing the entropy weight method to derive attribute weight information under Pythagorean fuzzy sets. This approach was then applied to RA for SRPs, showcasing a model grounded in the proposed methodology. Suresh and Dillibabu 27 proposed an innovative hybrid fuzzy-based machine learning mechanism tailored for RA in software projects. This hybrid scheme facilitated the identification and ranking of major software project risks, thereby supporting decision-making throughout the software project lifecycle. Akhavan et al. 28 introduced a Bayesian network modeling framework adept at capturing project risks by calculating the uncertainty of project net present value. This model provided an effective means for analyzing risk scenarios and their impact on project success, particularly applicable in evaluating risks for innovative projects that had undergone feasibility studies.

A review of factors affecting SRPs

Within the realm of SRPs management, the assessment and proficient management of project risks stand as imperative components. Consequently, a range of studies has been conducted to explore diverse methods and models aimed at enhancing the comprehension and decision support associated with project risks. Guan et al. 29 introduced a new risk interdependence network model based on Monte Carlo simulation to support decision-makers in more effectively assessing project risks and planning risk management actions. They integrated interpretive structural modeling methods into the model to develop a hierarchical project risk interdependence network based on identified risks and their causal relationships. Vujović et al. 30 provided a new method for research in project management through careful analysis of risk management in SRPs. To confirm the hypothesis, the study focused on educational organizations and outlined specific project management solutions in business systems, thereby improving the business and achieving positive business outcomes. Muñoz-La Rivera et al. 31 described and classified the 100 identified factors based on the dimensions and aspects of the project, assessed their impact, and determined whether they were shaping or directly affecting the occurrence of research project accidents. These factors and their descriptions and classifications made significant contributions to improving the security creation of the system and generating training and awareness materials, fostering the development of a robust security culture within organizations. Nguyen et al. concentrated on the pivotal risk factors inherent in design-build projects within the construction industry. Effective identification and management of these factors enhanced project success and foster confidence among owners and contractors in adopting the design-build approach 32 . Their study offers valuable insights into RA in project management and the adoption of new contract forms. Nguyen and Le delineated risk factors influencing the quality of 20 civil engineering projects during the construction phase 33 . The top five risks identified encompass poor raw material quality, insufficient worker skills, deficient design documents and drawings, geographical challenges at construction sites, and inadequate capabilities of main contractors and subcontractors. Meanwhile, Nguyen and Phu Pham concentrated on office building projects in Ho Chi Minh City, Vietnam, to pinpoint key risk factors during the construction phase 34 . These factors were classified into five groups based on their likelihood and impact: financial, management, schedule, construction, and environmental. Findings revealed that critical factors affecting office building projects encompassed both natural elements (e.g., prolonged rainfall, storms, and climate impacts) and human factors (e.g., unstable soil, safety behavior, owner-initiated design changes), with schedule-related risks exerting the most significant influence during the construction phase of Ho Chi Minh City’s office building projects. This provides construction and project management practitioners with fresh insights into risk management, aiding in the comprehensive identification, mitigation, and management of risk factors in office building projects.

While existing research has made notable strides in RA for SRPs, certain limitations persist. These studies limitations in quantifying the degree of influence of various factors and analyzing their interrelationships, thereby falling short of offering specific and actionable recommendations. Traditional methods, due to their inherent limitations, struggle to precisely quantify risk degrees and often overlook the intricate interplay among multiple factors. Consequently, there is an urgent need for a comprehensive method capable of quantifying the impact of diverse factors and revealing their correlations. In response to this exigency, this paper introduces the TANB model. The unique advantages of this algorithm in the RA of scientific and technological projects have been fully realized. Tailored to address the characteristics of uncertainty and complexity, the model represents a significant leap forward in enhancing applicability and accuracy. In comparison with traditional methods, the TANB model exhibits greater flexibility and a heightened ability to capture dependencies between features, thereby elevating the overall performance of RA. This innovative method emerges as a more potent and reliable tool in the realm of scientific and technological project management, furnishing decision-makers with more comprehensive and accurate support for RA.

Research methodology

This paper centers on the latest iteration of ISO 31000, delving into the project risk management process and scrutinizing the RA for SRPs and their intricate interplay with associated factors. ISO 31000, an international risk management standard, endeavors to furnish businesses, organizations, and individuals with a standardized set of risk management principles and guidelines, defining best practices and establishing a common framework. The paper unfolds in distinct phases aligned with ISO 31000:

Risk Identification: Employing data collection and preparation, a spectrum of factors related to project size, budget investment, team member experience, project duration, and technical difficulty were identified.

RA: Utilizing the Naive Bayes algorithm, the paper conducts RA for SRPs, estimating the probability distribution of various factors influencing RA results.

Risk Response: The application of the Naive Bayes model is positioned as a means to respond to risks, facilitating the formulation of apt risk response strategies based on calculated probabilities.

Monitoring and Control: Through meticulous data collection, model training, and verification, the paper illustrates the steps involved in monitoring and controlling both data and models. Regular monitoring of identified risks and responses allows for adjustments when necessary.

Communication and Reporting: Maintaining effective communication throughout the project lifecycle ensures that stakeholders comprehend the status of project risks. Transparent reporting on discussions and outcomes contributes to an informed project environment.

Data collection and preparation

In this paper, a meticulous approach is undertaken to select representative research project cases, adhering to stringent screening criteria. Additionally, a thorough review of existing literature is conducted and tailored to the practical requirements of SRPs management. According to Nguyen et al., these factors play a pivotal role in influencing the RA outcomes of SRPs 35 . Furthermore, research by He et al. underscored the significant impact of team members’ experience on project success 36 . Therefore, in alignment with our research objectives and supported by the literature, this paper identifies variables such as project scale, budget investment, team member experience, project duration, and technical difficulty as the focal themes. To ensure the universality and scientific rigor of our findings, the paper adheres to stringent selection criteria during the project case selection process. After preliminary screening of SRPs completed in the past 5 years, considering factors such as project diversity, implementation scales, and achieved outcomes, five representative projects spanning diverse fields, including engineering, medicine, and information technology, are ultimately selected. These project cases are chosen based on their capacity to represent various scales and types of SRPs, each possessing a typical risk management process, thereby offering robust and comprehensive data support for our study. The subsequent phase involves detailed data collection on each chosen project, encompassing diverse dimensions such as project scale, budget investment, team member experience, project cycle, and technical difficulty. The collected data undergo meticulous preprocessing to ensure data quality and reliability. The preprocessing steps comprised data cleaning, addressing missing values, handling outliers, culminating in the creation of a self-constructed dataset. The dataset encompasses over 500 SRPs across diverse disciplines and fields, ensuring statistically significant and universal outcomes. Particular emphasis is placed on ensuring dataset diversity, incorporating projects of varying scales, budgets, and team experience levels. This comprehensive coverage ensures the representativeness and credibility of the study on RA in SRPs. New influencing factors are introduced to expand the research scope, including project management quality (such as time management and communication efficiency), historical success rate, industry dynamics, and market demand. Detailed definitions and quantifications are provided for each new variable to facilitate comprehensive data processing and analysis. For project management quality, consideration is given to time management accuracy and communication frequency and quality among team members. Historical success rate is determined by reviewing past project records and outcomes. Industry dynamics are assessed by consulting the latest scientific literature and patent information. Market demand is gauged through market research and user demand surveys. The introduction of these variables enriches the understanding of RA in SRPs and opens up avenues for further research exploration.

At the same time, the collected data are integrated and coded in order to apply Naive Bayes algorithm and MLR analysis. For cases involving qualitative data, this paper uses appropriate coding methods to convert it into quantitative data for processing in the model. For example, for the qualitative feature of team member experience, numerical values are used to represent different experience levels, such as 0 representing beginners, 0 representing intermediate, and 2 representing advanced. The following is a specific sample data set example (Table 1 ). It shows the processed structured data, and the values in the table represent the specific characteristics of each project.

Establishment of naive Bayesian model

The Naive Bayesian algorithm, a probabilistic and statistical classification method renowned for its effectiveness in analyzing and predicting multi-dimensional data, is employed in this paper to conduct the RA for SRPs. The application of the Naive Bayesian algorithm to RA for SRPs aims to discern the influence of various factors on the outcomes of RA. The Naive Bayesian algorithm, depicted in Fig.  1 , operates on the principles of Bayesian theorem, utilizing posterior probability calculations for classification tasks. The fundamental concept of this algorithm hinges on the assumption of independence among different features, embodying the “naivety” hypothesis. In the context of RA for SRPs, the Naive Bayesian algorithm is instrumental in estimating the probability distribution of diverse factors affecting the RA results, thereby enhancing the precision of risk estimates. In the Naive Bayesian model, the initial step involves the computation of posterior probabilities for each factor, considering the given RA result conditions. Subsequently, the category with the highest posterior probability is selected as the predictive outcome.

Naive Bayesian algorithm process.

In Fig.  1 , the data collection process encompasses vital project details such as project scale, budget investment, team member experience, project cycle, technical difficulty, and RA results. This meticulous collection ensures the integrity and precision of the dataset. Subsequently, the gathered data undergoes integration and encoding to convert qualitative data into quantitative form, facilitating model processing and analysis. Tailored to specific requirements, relevant features are chosen for model construction, accompanied by essential preprocessing steps like standardization and normalization. The dataset is then partitioned into training and testing sets, with the model trained on the former and its performance verified on the latter. Leveraging the training data, a Naive Bayesian model is developed to estimate probability distribution parameters for various features across distinct categories. Ultimately, the trained model is employed to predict new project features, yielding RA results.

Naive Bayesian models, in this context, are deployed to forecast diverse project risk levels. Let X symbolize the feature vector, encompassing project scale, budget investment, team member experience, project cycle, and technical difficulty. The objective is to predict the project’s risk level, denoted as Y. Y assumes discrete values representing distinct risk levels. Applying the Bayesian theorem, the posterior probability P(Y|X) is computed, signifying the probability distribution of projects falling into different risk levels given the feature vector X. The fundamental equation governing the Naive Bayesian model is expressed as:

In Eq. ( 1 ), P(Y|X) represents the posterior probability, denoting the likelihood of the project belonging to a specific risk level. P(X|Y) signifies the class conditional probability, portraying the likelihood of the feature vector X occurring under known risk level conditions. P(Y) is the prior probability, reflecting the antecedent likelihood of the project pertaining to a particular risk level. P(X) acts as the evidence factor, encapsulating the likelihood of the feature vector X occurring.

The Naive Bayes, serving as the most elementary Bayesian network classifier, operates under the assumption of attribute independence given the class label c , as expressed in Eq. ( 2 ):

The classification decision formula for Naive Bayes is articulated in Eq. ( 3 ):

The Naive Bayes model, rooted in the assumption of conditional independence among attributes, often encounters deviations from reality. To address this limitation, the Tree-Augmented Naive Bayes (TANB) model extends the independence assumption by incorporating a first-order dependency maximum-weight spanning tree. TANB introduces a tree structure that more comprehensively models relationships between features, easing the constraints of the independence assumption and concurrently mitigating issues associated with multicollinearity. This extension bolsters its efficacy in handling intricate real-world data scenarios. TANB employs conditional mutual information \(I(X_{i} ;X_{j} |C)\) to gauge the dependency between attributes \(X_{j}\) and \(X_{i}\) , thereby constructing the maximum weighted spanning tree. In TANB, any attribute variable \(X_{i}\) is permitted to have at most one other attribute variable as its parent node, expressed as \(Pa\left( {X_{i} } \right) \le 2\) . The joint probability \(P_{con} \left( {x,c} \right)\) undergoes transformation using Eq. ( 4 ):

In Eq. ( 4 ), \(x_{r}\) refers to the root node, which can be expressed as Eq. ( 5 ):

TANB classification decision equation is presented below:

In the RA of SRPs, normal distribution parameters, such as mean (μ) and standard deviation (σ), are estimated for each characteristic dimension (project scale, budget investment, team member experience, project cycle, and technical difficulty). This estimation allows the calculation of posterior probabilities for projects belonging to different risk levels under given feature vector conditions. For each feature dimension \({X}_{i}\) , the mean \({mu}_{i,j}\) and standard deviation \({{\text{sigma}}}_{i,j}\) under each risk level are computed, where i represents the feature dimension, and j denotes the risk level. Parameter estimation employs the maximum likelihood method, and the specific calculations are as follows.

In Eqs. ( 7 ) and ( 8 ), \({N}_{j}\) represents the number of projects belonging to risk level j . \({x}_{i,k}\) denotes the value of the k -th item in the feature dimension i . Finally, under a given feature vector, the posterior probability of a project with risk level j is calculated as Eq. ( 9 ).

In Eq. ( 9 ), d represents the number of feature dimensions, and Z is the normalization factor. \(P(Y=j)\) represents the prior probability of category j . \(P({X}_{i}\mid Y=j)\) represents the normal distribution probability density function of feature dimension i under category j . The risk level of a project can be predicted by calculating the posterior probabilities of different risk levels to achieve RA for SRPs.

This paper integrates the probability estimation of the Naive Bayes model with actual project risk response strategies, enabling a more flexible and targeted response to various risk scenarios. Such integration offers decision support to project managers, enhancing their ability to address potential challenges effectively and ultimately improving the overall success rate of the project. This underscores the notion that risk management is not solely about problem prevention but stands as a pivotal factor contributing to project success.

MLR analysis

MLR analysis is used to validate the hypothesis to deeply explore the impact of various factors on RA of SRPs. Based on the previous research status, the following research hypotheses are proposed.

Hypothesis 1: There is a positive relationship among project scale, budget investment, and team member experience and RA results. As the project scale, budget investment, and team member experience increase, the RA results also increase.

Hypothesis 2: There is a negative relationship between the project cycle and the RA results. Projects with shorter cycles may have higher RA results.

Hypothesis 3: There is a complex relationship between technical difficulty and RA results, which may be positive, negative, or bidirectional in some cases. Based on these hypotheses, an MLR model is established to analyze the impact of factors, such as project scale, budget investment, team member experience, project cycle, and technical difficulty, on RA results. The form of an MLR model is as follows.

In Eq. ( 10 ), Y represents the RA result (dependent variable). \({X}_{1}\) to \({X}_{5}\) represent factors, such as project scale, budget investment, team member experience, project cycle, and technical difficulty (independent variables). \({\beta }_{0}\) to \({\beta }_{5}\) are the regression coefficients, which represent the impact of various factors on the RA results. \(\epsilon\) represents a random error term. The model structure is shown in Fig.  2 .

Schematic diagram of an MLR model.

In Fig.  2 , the MLR model is employed to scrutinize the influence of various independent variables on the outcomes of RA. In this specific context, the independent variables encompass project size, budget investment, team member experience, project cycle, and technical difficulty, all presumed to impact the project’s RA results. Each independent variable is denoted as a node in the model, with arrows depicting the relationships between these factors. In an MLR model, the arrow direction signifies causality, illustrating the influence of an independent variable on the dependent variable.

When conducting MLR analysis, it is necessary to estimate the parameter \(\upbeta\) in the regression model. These parameters determine the relationship between the independent and dependent variables. Here, the Ordinary Least Squares (OLS) method is applied to estimate these parameters. The OLS method is a commonly used parameter estimation method aimed at finding parameter values that minimize the sum of squared residuals between model predictions and actual observations. The steps are as follows. Firstly, based on the general form of an MLR model, it is assumed that there is a linear relationship between the independent and dependent variables. It can be represented by a linear equation, which includes regression coefficients β and the independent variable X. For each observation value, the difference between its predicted and actual values is calculated, which is called the residual. Residual \({e}_{i}\) can be expressed as:

In Eq. ( 11 ), \({Y}_{i}\) is the actual observation value, and \({\widehat{Y}}_{i}\) is the value predicted by the model. The goal of the OLS method is to adjust the regression coefficients \(\upbeta\) to minimize the sum of squared residuals of all observations. This can be achieved by solving an optimization problem, and the objective function is the sum of squared residuals.

Then, the estimated value of the regression coefficient \(\upbeta\) that minimizes the sum of squared residuals can be obtained by taking the derivative of the objective function and making the derivative zero. The estimated values of the parameters can be obtained by solving this system of equations. The final estimated regression coefficient can be expressed as:

In Eq. ( 13 ), X represents the independent variable matrix. Y represents the dependent variable vector. \(({X}^{T}X{)}^{-1}\) is the inverse of a matrix, and \(\widehat{\beta }\) is a parameter estimation vector.

Specifically, solving for the estimated value of regression coefficient \(\upbeta\) requires matrix operation and statistical analysis. Based on the collected project data, substitute it into the model and calculate the residual. Then, the steps of the OLS method are used to obtain parameter estimates. These parameter estimates are used to establish an MLR model to predict RA results and further analyze the influence of different factors.

The degree of influence of different factors on the RA results can be determined by analyzing the value of the regression coefficient β. A positive \(\upbeta\) value indicates that the factor has a positive impact on the RA results, while a negative \(\upbeta\) value indicates that the factor has a negative impact on the RA results. Additionally, hypothesis testing can determine whether each factor is significant in the RA results.

The TANB model proposed in this paper extends the traditional naive Bayes model by incorporating conditional dependencies between attributes to enhance the representation of feature interactions. While the traditional naive Bayes model assumes feature independence, real-world scenarios often involve interdependencies among features. To address this, the TANB model is introduced. The TANB model introduces a tree structure atop the naive Bayes model to more accurately model feature relationships, overcoming the limitation of assuming feature independence. Specifically, the TANB model constructs a maximum weight spanning tree to uncover conditional dependencies between features, thereby enabling the model to better capture feature interactions.

Assessment indicators

To comprehensively assess the efficacy of the proposed TANB model in the RA for SRPs, a self-constructed dataset serves as the data source for this experimental evaluation, as outlined in Table 1 . The dataset is segregated into training (80%) and test sets (20%). These indicators cover the accuracy, precision, recall rate, F1 value, and Area Under the Curve (AUC) Receiver Operating Characteristic (ROC) of the model. The following are the definitions and equations for each assessment indicator. Accuracy is the proportion of correctly predicted samples to the total number of samples. Precision is the proportion of Predicted Positive (PP) samples to actual positive samples. The recall rate is the proportion of correctly PP samples among the actual positive samples. The F1 value is the harmonic average of precision and recall, considering the precision and comprehensiveness of the model. The area under the ROC curve measures the classification performance of the model, and a larger AUC value indicates better model performance. The ROC curve suggests the relationship between True Positive Rate and False Positive Rate under different thresholds. The AUC value can be obtained by accumulating the area of each small rectangle under the ROC curve. The confusion matrix is used to display the prediction property of the model in different categories, including True Positive (TP), True Negative (TN), False Positive (FP), and False Negative (FN).

The performance of TANB in RA for SRPs can be comprehensively assessed to understand the advantages, disadvantages, and applicability of the model more comprehensively by calculating the above assessment indicators.

Results and discussion

Accuracy analysis of naive bayesian algorithm.

On the dataset of this paper, Fig.  3 reveals the performance of TANB algorithm under different assessment indicators.

Performance assessment of TANB algorithm on different projects.

From Fig.  3 , the TANB algorithm performs well in various projects, ranging from 0.87 to 0.911 in accuracy. This means that the overall accuracy of the model in predicting project risks is quite high. The precision also maintains a high level in various projects, ranging from 0.881 to 0.923, indicating that the model performs well in classifying high-risk categories. The recall rate ranges from 0.872 to 0.908, indicating that the model can effectively capture high-risk samples. Meanwhile, the AUC values in each project are relatively high, ranging from 0.905 to 0.931, which once again emphasizes the effectiveness of the model in risk prediction. From multiple assessment indicators, such as accuracy, precision, recall, F1 value, and AUC, the TANB algorithm has shown good risk prediction performance in representative projects. The performance assessment results of the TANB algorithm under different feature dimensions are plotted in Figs.  4 , 5 , 6 and 7 .

Prediction accuracy of TANB algorithm on different budget investments.

Prediction accuracy of TANB algorithm on different team experiences.

Prediction accuracy of TANB algorithm at different risk levels.

Prediction accuracy of TANB algorithm on different project scales.

From Figs.  4 , 5 , 6 and 7 , as the level of budget investment increases, the accuracy of most projects also shows an increasing trend. Especially in cases of high budget investment, the accuracy of the project is generally high. This may mean that a higher budget investment helps to reduce project risks, thereby improving the prediction accuracy of the TANB algorithm. It can be observed that team experience also affects the accuracy of the model. Projects with high team experience exhibit higher accuracy in TANB algorithms. This may indicate that experienced teams can better cope with project risks to improve the performance of the model. When budget investment and team experience are low, accuracy is relatively low. This may imply that budget investment and team experience can complement each other to affect the model performance.

There are certain differences in the accuracy of projects under different risk levels. Generally speaking, the accuracy of high-risk and medium-risk projects is relatively high, while the accuracy of low-risk projects is relatively low. This may be because high-risk and medium-risk projects require more accurate predictions, resulting in higher accuracy. Similarly, project scale also affects the performance of the model. Large-scale and medium-scale projects exhibit high accuracy in TANB algorithms, while small-scale projects have relatively low accuracy. This may be because the risks of large-scale and medium-scale projects are easier to identify and predict to promote the performance of the model. In high-risk and large-scale projects, accuracy is relatively high. This may indicate that the impact of project scale is more significant in specific risk scenarios.

Figure  8 further compares the performance of the TANB algorithm proposed here with other similar algorithms.

Performance comparison of different algorithms in RA of SRPs.

As depicted in Fig.  8 , the TANB algorithm attains an accuracy and precision of 0.912 and 0.920, respectively, surpassing other algorithms. It excels in recall rate and F1 value, registering 0.905 and 0.915, respectively, outperforming alternative algorithms. These findings underscore the proficiency of the TANB algorithm in comprehensively identifying high-risk projects while sustaining high classification accuracy. Moreover, the algorithm achieves an AUC of 0.930, indicative of its exceptional predictive prowess in sample classification. Thus, the TANB algorithm exhibits notable potential for application, particularly in scenarios demanding the recognition and comprehensiveness requisite for high-risk project identification. The evaluation results of the TANB model in predicting project risk levels are presented in Table 2 :

Table 2 demonstrates that the TANB model surpasses the traditional Naive Bayes model across multiple evaluation metrics, including accuracy, precision, and recall. This signifies that, by accounting for feature interdependence, the TANB model can more precisely forecast project risk levels. Furthermore, leveraging the model’s predictive outcomes, project managers can devise tailored risk mitigation strategies corresponding to various risk scenarios. For example, in high-risk projects, more assertive measures can be implemented to address risks, while in low-risk projects, risks can be managed more cautiously. This targeted risk management approach contributes to enhancing project success rates, thereby ensuring the seamless advancement of SRPs.

The exceptional performance of the TANB model in specific scenarios derives from its distinctive characteristics and capabilities. Firstly, compared to traditional Naive Bayes models, the TANB model can better capture the dependencies between attributes. In project RA, project features often exhibit complex interactions. The TANB model introduces first-order dependencies between attributes, allowing features to influence each other, thereby more accurately reflecting real-world situations and improving risk prediction precision. Secondly, the TANB model demonstrates strong adaptability and generalization ability in handling multidimensional data. SRPs typically involve data from multiple dimensions, such as project scale, budget investment, and team experience. The TANB model effectively processes these multidimensional data, extracts key information, and achieves accurate RA for projects. Furthermore, the paper explores the potential of using hybrid models or ensemble learning methods to further enhance model performance. By combining other machine learning algorithms, such as random forests and support vector regressors with sigmoid kernel, through ensemble learning, the shortcomings of individual models in specific scenarios can be overcome, thus improving the accuracy and robustness of RA. For example, in the study, we compared the performance of the TANB model with other algorithms in RA, as shown in Table 3 .

Table 3 illustrates that the TANB model surpasses other models in terms of accuracy, precision, recall, F1 value, and AUC value, further confirming its superiority and practicality in RA. Therefore, the TANB model holds significant application potential in SRPs, offering effective decision support for project managers to better evaluate and manage project risks, thereby enhancing the likelihood of project success.

Analysis of the degree of influence of different factors

Table 4 analyzes the degree of influence and interaction of different factors.

In Table 4 , the regression analysis results reveal that budget investment and team experience exert a significantly positive impact on RA outcomes. This suggests that increasing budget allocation and assembling a team with extensive experience can enhance project RA outcomes. Specifically, the regression coefficient for budget investment is 0.68, and for team experience, it is 0.51, both demonstrating significant positive effects (P < 0.05). The P-values are all significantly less than 0.05, indicating a significant impact. The impact of project scale is relatively small, at 0.31, and its P-value is also much less than 0.05. The degree of interaction influence is as follows. The impact of interaction terms is also significant, especially the interaction between budget investment and team experience and the interaction between budget investment and project scale. The P value of the interaction between budget investment and project scale is 0.002, and the P value of the interaction between team experience and project scale is 0.003. The P value of the interaction among budget investment, team experience, and project scale is 0.005. So, there are complex relationships and interactions among different factors, and budget investment and team experience significantly affect the RA results. However, the budget investment and project scale slightly affect the RA results. Project managers should comprehensively consider the interactive effects of different factors when making decisions to more accurately assess the risks of SRPs.

The interaction between team experience and budget investment

The results of the interaction between team experience and budget investment are demonstrated in Table 5 .

From Table 5 , the degree of interaction impact can be obtained. Budget investment and team experience, along with the interaction between project scale and technical difficulty, are critical factors in risk mitigation. Particularly in scenarios characterized by large project scales and high technical difficulties, adequate budget allocation and a skilled team can substantially reduce project risks. As depicted in Table 5 , under conditions of high team experience and sufficient budget investment, the average RA outcome is 0.895 with a standard deviation of 0.012, significantly lower than assessment outcomes under other conditions. This highlights the synergistic effects of budget investment and team experience in effectively mitigating risks in complex project scenarios. The interaction between team experience and budget investment has a significant impact on RA results. Under high team experience, the impact of different budget investment levels on RA results is not significant, but under medium and low team experience, the impact of different budget investment levels on RA results is significantly different. The joint impact of team experience and budget investment is as follows. Under high team experience, the impact of budget investment is relatively small, possibly because high-level team experience can compensate for the risks brought by insufficient budget to some extent. Under medium and low team experience, the impact of budget investment is more significant, possibly because the lack of team experience makes budget investment play a more important role in RA. Therefore, team experience and budget investment interact in RA of SRPs. They need to be comprehensively considered in project decision-making. High team experience can compensate for the risks brought by insufficient budget to some extent, but in the case of low team experience, the impact of budget investment on RA is more significant. An exhaustive consideration of these factors and their interplay is imperative for effectively assessing the risks inherent in SRPs. Merely focusing on budget allocation or team expertise may not yield a thorough risk evaluation. Project managers must scrutinize the project’s scale, technical complexity, and team proficiency, integrating these aspects with budget allocation and team experience. This holistic approach fosters a more precise RA and facilitates the development of tailored risk management strategies, thereby augmenting the project’s likelihood of success. In conclusion, acknowledging the synergy between budget allocation and team expertise, in conjunction with other pertinent factors, is pivotal in the RA of SRPs. Project managers should adopt a comprehensive outlook to ensure sound decision-making and successful project execution.

Risk mitigation strategies

To enhance the discourse on project risk management in this paper, a dedicated section on risk mitigation strategies has been included. Leveraging the insights gleaned from the predictive model regarding identified risk factors and their corresponding risk levels, targeted risk mitigation measures are proposed.

Primarily, given the significant influence of budget investment and team experience on project RA outcomes, project managers are advised to prioritize these factors and devise pertinent risk management strategies.

For risks stemming from budget constraints, the adoption of flexible budget allocation strategies is advocated. This may involve optimizing project expenditures, establishing financial reserves, or seeking additional funding avenues.

In addressing risks attributed to inadequate team experience, measures such as enhanced training initiatives, engagement of seasoned project advisors, or collaboration with experienced teams can be employed to mitigate the shortfall in expertise.

Furthermore, recognizing the impact of project scale, duration, and technical complexity on RA outcomes, project managers are advised to holistically consider these factors during project planning. This entails adjusting project scale as necessary, establishing realistic project timelines, and conducting thorough assessments of technical challenges prior to project commencement.

These risk mitigation strategies aim to equip project managers with a comprehensive toolkit for effectively identifying, assessing, and mitigating risks inherent in SRPs.

This paper delves into the efficacy of the TANB algorithm in project risk prediction. The findings indicate that the algorithm demonstrates commendable performance across diverse projects, boasting high precision, recall rates, and AUC values, thereby outperforming analogous algorithms. This aligns with the perspectives espoused by Asadullah et al. 37 . Particular emphasis was placed on assessing the impact of variables such as budget investment levels, team experience, and project size on algorithmic performance. Notably, heightened budget investment and extensive team experience positively influenced the results, with project size exerting a comparatively minor impact. Regression analysis elucidates the magnitude and interplay of these factors, underscoring the predominant influence of budget investment and team experience on RA outcomes, whereas project size assumes a relatively marginal role. This underscores the imperative for decision-makers in projects to meticulously consider the interrelationships between these factors for a more precise assessment of project risks, echoing the sentiments expressed by Testorelli et al. 38 .

In sum, this paper furnishes a holistic comprehension of the Naive Bayes algorithm’s application in project risk prediction, offering robust guidance for practical project management. The paper’s tangible applications are chiefly concentrated in the realm of RA and management for SRPs. Such insights empower managers in SRPs to navigate risks with scientific acumen, thereby enhancing project success rates and performance. The paper advocates several strategic measures for SRPs management: prioritizing resource adjustments and team training to elevate the professional skill set of team members in coping with the impact of team experience on risks; implementing project scale management strategies to mitigate potential risks by detailed project stage division and stringent project planning; addressing technical difficulty as a pivotal risk factor through assessment and solution development strategies; incorporating project cycle adjustment and flexibility management to accommodate fluctuations and mitigate associated risks; and ensuring the integration of data quality management strategies to bolster data reliability and enhance model accuracy. These targeted risk responses aim to improve the likelihood of project success and ensure the seamless realization of project objectives.

Achievements

In this paper, the application of Naive Bayesian algorithm in RA of SRPs is deeply explored, and the influence of various factors on RA results and their relationship is comprehensively investigated. The research results fully prove the good accuracy and applicability of Naive Bayesian algorithm in RA of science and technology projects. Through probability estimation, the risk level of the project can be estimated more accurately, which provides a new decision support tool for the project manager. It is found that budget input and team experience are the most significant factors affecting the RA results, and their regression coefficients are 0.68 and 0.51 respectively. However, the influence of project scale on the RA results is relatively small, and its regression coefficient is 0.31. Especially in the case of low team experience, the budget input has a more significant impact on the RA results. However, it should also be admitted that there are some limitations in the paper. First, the case data used is limited and the sample size is relatively small, which may affect the generalization ability of the research results. Second, the factors concerned may not be comprehensive, and other factors that may affect RA, such as market changes and policies and regulations, are not considered.

The paper makes several key contributions. Firstly, it applies the Naive Bayes algorithm to assess the risks associated with SRPs, proposing the TANB and validating its effectiveness empirically. The introduction of the TANB model broadens the application scope of the Naive Bayes algorithm in scientific research risk management, offering novel methodologies for project RA. Secondly, the study delves into the impact of various factors on RA for SRPs through MLR analysis, highlighting the significance of budget investment and team experience. The results underscore the positive influence of budget investment and team experience on RA outcomes, offering valuable insights for project decision-making. Additionally, the paper examines the interaction between team experience and budget investment, revealing a nuanced relationship between the two in RA. This finding underscores the importance of comprehensively considering factors such as team experience and budget investment in project decision-making to achieve more accurate RA. In summary, the paper provides crucial theoretical foundations and empirical analyses for SRPs risk management by investigating RA and its influencing factors in depth. The research findings offer valuable guidance for project decision-making and risk management, bolstering efforts to enhance the success rate and efficiency of SRPs.

This paper distinguishes itself from existing research by conducting an in-depth analysis of the intricate interactions among various factors, offering more nuanced and specific RA outcomes. The primary objective extends beyond problem exploration, aiming to broaden the scope of scientific evaluation and research practice through the application of statistical language. This research goal endows the paper with considerable significance in the realm of science and technology project management. In comparison to traditional methods, this paper scrutinizes project risk with greater granularity, furnishing project managers with more actionable suggestions. The empirical analysis validates the effectiveness of the proposed method, introducing a fresh perspective for decision-making in science and technology projects. Future research endeavors will involve expanding the sample size and accumulating a more extensive dataset of SRPs to enhance the stability and generalizability of results. Furthermore, additional factors such as market demand and technological changes will be incorporated to comprehensively analyze elements influencing the risks of SRPs. Through these endeavors, the aim is to provide more precise and comprehensive decision support to the field of science and technology project management, propelling both research and practice in this domain to new heights.

Limitations and prospects

This paper, while employing advanced methodologies like TANB models, acknowledges inherent limitations that warrant consideration. Firstly, like any model, TANB has its constraints, and predictions in specific scenarios may be subject to these limitations. Subsequent research endeavors should explore alternative advanced machine learning and statistical models to enhance the precision and applicability of RA. Secondly, the focus of this paper predominantly centers on the RA for SRPs. Given the unique characteristics and risk factors prevalent in projects across diverse fields and industries, the generalizability of the paper results may be limited. Future research can broaden the scope of applicability by validating the model across various fields and industries. The robustness and generalizability of the model can be further ascertained through the incorporation of extensive real project data in subsequent research. Furthermore, future studies can delve into additional data preprocessing and feature engineering methods to optimize model performance. In practical applications, the integration of research outcomes into SRPs management systems could provide more intuitive and practical support for project decision-making. These avenues represent valuable directions for refining and expanding the contributions of this research in subsequent studies.

Data availability

All data generated or analysed during this study are included in this published article [and its Supplementary Information files].

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Xuying Dong and Wanlin Qiu played a key role in the writing of Risk Assessment of Scientific Research Projects and the Relationship between Related Factors Based on Naive Bayes Algorithm. First, they jointly developed clearly defined research questions and methods for risk assessment using the naive Bayes algorithm at the beginning of the research project. Secondly, Xuying Dong and Wanlin Qiu were responsible for data collection and preparation, respectively, to ensure the quality and accuracy of the data used in the research. They worked together to develop a naive Bayes algorithm model, gain a deep understanding of the algorithm, ensure the effectiveness and performance of the model, and successfully apply the model in practical research. In the experimental and data analysis phase, the collaborative work of Xuying Dong and Wanlin Qiu played a key role in verifying the validity of the model and accurately assessing the risks of the research project. They also collaborated on research papers, including detailed descriptions of methods, experiments and results, and actively participated in the review and revision process, ensuring the accuracy and completeness of the findings. In general, the joint contribution of Xuying Dong and Wanlin Qiu has provided a solid foundation for the success of this research and the publication of high-quality papers, promoted the research on the risk assessment of scientific research projects and the relationship between related factors, and made a positive contribution to the progress of the field.

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Dong, X., Qiu, W. A case study on the relationship between risk assessment of scientific research projects and related factors under the Naive Bayesian algorithm. Sci Rep 14 , 8244 (2024). https://doi.org/10.1038/s41598-024-58341-y

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4 Hypotheses Testing in Banking Risk Analysis

• Published: May 2022
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A risk manager requires taking a decision to select a single alternative from a number of possible alternatives. In this context, hypothesis testing provides a formal procedure for making rational decision based on the information available to the researcher. In this chapter, the author explains the statistical approach to hypothesis testing and relates its relevance to management of risk. It covers statistical concept behind hypothesis testing, type I error, and power of a test. It enables the reader to understand and interpret statistical significance tests. It covers both one-tail as well as two-tail tests. Statistical significance through z -test as well as t -tests is shown with numerous applications in risk management. Parametric as well as non-parametric test concepts, formulas, and their application in statistical package like STATA have been demonstrated. Two group difference mean t -test and rank-sum tests (treatment group vs. control group) and ANOVA test for multiple groups mean comparison tests have been explained with examples.

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Current Theories of Risk and Rational Decision Making

Valerie f. reyna.

Departments of Human Development and Psychology; Center for Behavioral Economics and Decision Research, Cornell University

Susan E. Rivers

Department of Psychology, Yale University and Department of Human Development, Cornell University

There are few topics that are more important than risk and rational decision making, as the contributions to this special issue attest. If we contemplate the risks and consequences of smoking, substance use, reckless driving, violent crime, and unprotected sex, we cannot help but conjure up an image of the stereotypical, irrational risk taker: the adolescent. Statistics confirm that adolescents and young adults are disproportionately responsible for carnage on the highway, new cases of HIV/AIDS, initiation of poor lifestyle choices such as smoking and unhealthy eating, and a host of other risk-taking behaviors that pose challenges for the law, public health, clinical psychology, and public policy ( Reyna & Farley, 2006 ). Therefore, it is not surprising that the articles contained in this issue on risk and rational decision making focus on adolescence, which had been neglected until the recent flurry of work on this time of life.

Although the focus is on adolescence, and on the developmental differences between adolescents and other age groups, the implications of this body of work are far-reaching. Each contributor has articulated a theoretical framework that is guiding the science of risky behavior in new directions, albeit from varied perspectives (e.g., emphasizing cognitive, social, emotional, public health, or behavioral neuroscience approaches). The discussant, a distinguished legal scholar, has ably integrated the papers and identified key theoretical and policy implications. Theories of adult behavior must take account of these perspectives or leave themselves open to the obvious criticisms that they are (a) incomplete because they ignore the origins of behavior and (b) irrelevant because they ignore major causes of death and human suffering. Thus, this special issue provides an authoritative review of developmental research on risk and rational decision making, with fundamental implications for theories of reasoning, judgment, and decision making, especially neurobiological and dual-process theories.

Adolescent Risk Taking and the Science of Judgment and Decision Making

Before moving on to the specific contributions to this issue, we want to say a word or two about how research on adolescent risk taking fits into the larger enterprise of judgment-and-decision-making research. The study of judgment and decision making has emerged as a field at the intersection of important problems in law, medicine, economics, and business. Major thinkers in this field have been awarded Nobel prizes for their work, including Maurice Allais, Herbert Simon, and Daniel Kahneman. As these lists suggest, research has focused most particularly on risk and uncertainty.

Two basic research strategies or approaches to doing science have been applied to the study of risk and uncertainty: The first, which characterizes work appearing in prominent adult journals (e.g., Psychological Science , Journal of Experimental Psychology: Learning, Memory, and Cognition , and Psychonomic Bulletin & Review ), mainly concerns the psychology of the college sophomore. That is, it consists of experiments conducted with young adults that are aimed at understanding the processes that control their behavior in laboratory analogies of everyday risk taking, such as the well-known framing problem as well as other games and gambling tasks. The other approach is aimed at understanding the processes that control the behavior of various subject populations for whom risk is part of their “job description” (i.e., who are engaged in risk taking as a matter of course): insurers, stock traders, emergency-room physicians, attorneys working on contingency fees, military and political leaders, intelligence and special forces officers, race car drivers, mountain climbers, and others. Although studying these populations tells us about risk taking, the problem is that these categories of people might be peculiar in some way. Being in these roles is the result of a self-selection (and other-selection) process; only peculiar people might get into these roles in the first place.

Adolescents, however, provide a normative sample of people for whom risk taking is a preoccupation of daily life. Moreover, as the articles in this special issue demonstrate, it is possible to conduct high-quality research that takes both approaches to doing science: Laboratory studies can be, and have been, conducted with adolescent samples, but studies have also been conducted that follow the adolescent into the real world of drinking, driving, drug taking, and sexually transmitted disease. Thus, the work in this issue is an example of an approach that combines the best of both worlds: basic science, including basic theories that apply to adult decision making, and applied science, including real-world risk taking. It is also an example of a special approach that eliminates a potential problem. By selecting a time of life at which risk taking is normal (and is at a high-water mark), we avoid many of the problems of selection bias. Just as memory problems are a hallmark of aging (and so it is natural to study memory processes in aging), problems with risk taking are characteristic of adolescence, and thus it is natural to study these problems in adolescence. One might say that adolescents are the “drosophila” of risk-taking research because they are such a natural preparation for understanding this fundamentally human phenomenon.

Behavioral Decision Making Framework

As an inheritor of the dominant expectancy-value approach in judgment-and-decision-making, and a pioneer in research on adolescent risky decision making, it is fitting to begin with the work of Baruch Fischhoff. In this issue, Fischhoff (2008) makes a compelling case for the behavioral decision making framework, emphasizing assessment of decision-making competence and providing a clear-eyed analysis of the components of this competence. Readers will find this article very useful; it is a succinct yet comprehensive description of an approach that has produced empirical breakthroughs concerning both adult and adolescent risky decision making. Among these findings is the noteworthy and now replicated finding that adolescents do not consider themselves to be invulnerable, exploding a myth that was once “received wisdom” and that continues to be believed by many practitioners and policy makers despite the evidence against it (e.g., Quadrel, Fischhoff, & Davis, 1993 ; see also Millstein & Halpern-Felsher, 2002 ). Table 1 in Fischhhoff's article provides additional evidence against the invulnerability hypothesis, showing that adolescents overestimate a myriad of risks to themselves, including their own mortality (data are derived from Bruine de Bruin, Parker, & Fischhoff, 2007 ). Although overestimation of risks is not an invariant finding, nevertheless, these findings join a growing number of findings showing that adolescents do not believe that they are immortal, but, on the contrary, they envision an unduly premature death (see also Reyna & Farley, 2006 , Figure 12; Jamieson & Romer, 2008 ). To be sure, Fischhoff ascribes the latter findings more to measurement error and adolescents' inability to skillfully use numerical response scales rather than to their real beliefs (“mortality judgments are anomalous”). It is a measure of how far the debate has shifted, however, that we are discussing the degree to which adolescents' overestimation, as opposed to underestimation, of risk is real.

A great variety of decisions can be described using the components of the behavioral decision-making framework, as Fischhoff (2008) well illustrates. Furthermore, guidance is provided on proper assessment of these components, namely, how to assess subjective probabilities (what adolescents believe) and values (what adolescents want or prefer). Fischhoff explains how values can be extracted through decision analysis if preferences are well-articulated or through methods that encourage reflection if they are not (e.g., the value elicitation approach). Although subjective probabilities and values constitute the basic building blocks of the behavioral decision-making framework, Fischhoff shows how social and affective factors can have influences on behavior via these constructs. Thus, this approach is powerful but relatively unconstrained. It can accommodate a variety of “theories” and possible results. For example, Fischhoff discusses how the framework accommodates multiple factors—and more factors could be added--that possibly influence how adolescents discount future outcomes (analogous to Frederick, Loewenstein, & O'Donoghue's, 2002 , seven proposed factors; Table 2, Fischhoff). As Fischhoff concludes, “From a behavioral decision research perspective, there can be no simple answer.”

Prototype-Willingness Model

Like the behavioral decision-making framework, the prototype-willingness model of Gerrard, Gibbons and associates (2008) is descended from expectancy-value approaches, in particular, the theories of reasoned action and of planned behavior. In addition to beliefs and values, the latter theories include perceptions of control, social norms, and self-efficacy in determining behavioral intentions, which are then used to predict behavior. Although much research on adolescent risk taking has been guided by such “deliberative” theories, newer approaches such as the prototype-willingness model emphasize the “less deliberative modes of decision making.” The concept of “willingness” captures, in part, what is meant by less deliberative modes of decision making. Willingness appears to be a more sensitive measure than either intention or expectation. Adolescents will divulge that they are willing to engage in socially less acceptable behaviors even when they deny that they intend or expect to engage in those behaviors, and willingness is associated with a greater tendency to take risks.

Although earlier deliberative models had multiple components, they assumed a single mode of analytical processing. Analytical processing could be engaged in well or poorly, and it was assumed to be subject to a “garbage in-garbage out” constraint on reasoning, namely, that if beliefs were faulty, decisions would be faulty. Lack of information, or combining information incorrectly, could also lead to poor decisions, as in the behavioral decision-making framework. But a single kind of thinking was assumed. In contrast, the prototype-willingness model is a dual-process model, a feature shared by Casey, Getz, and Galvan's (2008) developmental cognitive neuroscience approach, by Steinberg's (2008) social neuroscience approach, and by Rivers, Reyna, and Mills' (2008) fuzzy-trace theory. According to the prototype-willingness model, there is a reasoned path to adolescent risk taking (incorporating assumptions from the theories of reasoned action and planned behavior) and “a social reaction path that is image-based and involves more heuristic processing.” Although intention is the product of the reasoned path, willingness is the product of the reactive path. Prototypes are the images of typical members of social categories (e.g., smokers or non-smokers). Similar to the concept of gist in fuzzy-trace theory (derived from earlier cognitive constructs such as prototypes and schemas), images also have positive or negative valences. The more favorable an image (e.g., of smokers), the more willing adolescents seem to be to accept the social costs associated with engaging in risky behaviors (e.g., smoking).

Gerrard et al. (2008) offer an encyclopedic overview of evidence gathered to-date in the tradition of theories of reasoned action and related models, such as the prototype-willingness model, especially with respect to developmental issues. Their model is more encompassing than internal factors, such as willingness and prototypes. They also incorporate external factors, such as media exposure to alcohol and violence (which affects prototype favorability) and accessibility to alcohol and drugs in neighborhoods (which affects risk opportunity). Not surprisingly, willingness is more strongly tied to risk taking in environments in which substances and other temptations are accessible. As Gerrard et al. so pithily put it, “When few substances were available, adolescent willingness did not result in much use.” This result reinforces the importance of the context in which risky activities occur, as Steinberg (2008) argues. However, as we shall discuss, behavioral decision-making and dual-process theories differ from neurobiological approaches in their emphasis on interventions, on changing the individual as well as changing the environment.

Developmental Cognitive Neuroscience Framework

Casey, Getz, and Galvan (2008) also propose a dual-process model, but one that is derived from recent human imaging and animal studies. Three kinds of neuroimaging evidence are reviewed: structural MRI, which is used to measure the size and shape of brain structures; functional MRI which is used to measure patterns of brain activity; and diffusion tensor imaging (DTI) which is used to trace connectivity of white-matter fiber tracts. Despite the inherent challenges, Casey et al. make this material accessible to a broad audience. Behavioral researchers looking for a readable and integrative overview of research on risk taking and the adolescent brain, written by experts in the field, will find that this article fills the bill. Moreover, it is apparent from this overview that research in behavioral neuroscience is in the mainstream of work on adolescent risk taking, essential for understanding social, emotional, and cognitive mechanisms of development—and for understanding the challenges that human biology poses for public health interventions.

As Casey et al. (2008) discuss, there is broad consensus among developmental researchers that cognitive control (inhibition) increases with age across childhood and adolescence, and that this increase is associated with maturation of the prefrontal cortex. The importance of cognitive control is distilled by Casey et al. into a statement that is redolent with implications for social, emotional, cognitive, and biological development: “A cornerstone of cognitive development is the ability to suppress inappropriate thoughts and actions in favor of goal-directed ones, especially in the presence of compelling incentives.” As suggested by this statement, there are few major applied problems in education, mental health, or law enforcement that are not directly tied to this ability.

Casey et al. (2008) rely on emerging neurobiological evidence concerning developmental differences, knitting disparate sources of evidence together. Dual processes are substantiated, in part, by findings showing differential development across brain regions: Although the prefrontal cortex, crucial to cognitive control, matures relatively slowly from childhood through adolescence, subcortical regions mature relatively quickly. Neuroimaging studies of reward-related processing have homed in on a subcortical region called the nucleus accumbens, a portion of the basal ganglia involved in the anticipation of rewards. Recent research has shown that adolescents have enhanced accumbens activity in response to rewards, compared to either children or adults. Thus, in Casey et al.'s model, adolescent risk taking is the result of an unequal competition between immature, top-down control from the prefrontal cortex and heightened activation in subcortical reward areas (reflecting heightened responsiveness to rewards; see Figure 1 in Casey et al.). Top-down control in adolescence is further undermined by delayed functional connectivity between these prefrontal cortical and limbic subcortical regions.

Further, Galvan et al. (2007) showed that, across age, individual differences in risk taking were associated with greater activation in the nucleus accumbens. The flip side of cognitive control is impulsivity (i.e., difficulty with inhibition), which was also found to differ across age. Impulsivity, however, was not associated with accumbens activation. This pattern of findings is consistent with recent work showing that impulsivity (or delay of gratification) is empirically distinguishable from preferences for risk taking ( Green & Myerson, 2004 ; Myerson, Green, Hanson, Holt, & Estle, 2003 ; see also Reyna & Farley, 2006 ). Therefore, although words such as “impulsive” and “risk-seeking” have been used almost interchangeably to describe adolescent behavior, Casey et al. review evidence supporting the conclusion that “these constructs rely on different cognitive and neural processes.”

Developmental Social Neuroscience Framework

Steinberg (2008) summarizes, organizes, and interprets a wealth of data, ranging from effects of gonadal hormones at puberty (on the proliferation of receptors for oxytocin, implicated in social bonding) to neuroimaging of anger (that individuals who are susceptible to peer influence may be unusually aroused by anger in others but less able to inhibit their responses). He ties this variegated evidence together using a dual-process model pitting cognitive control against socio-emotional systems. (Risk taking decreases because of the former and it increases because of the latter.) Like Casey et al. (2008) , Steinberg premises his dual-process approach on the observation that risk-taking appears to increase between childhood and adolescence, and to later decrease in adulthood. Linear or monotonic trends in cognitive control are not sufficient to explain such trends because, by themselves, they predict that children ought to be more risk-seeking than adolescents (assuming that all other factors are equal, such as risk opportunity).

Steinberg (2008) argues that logical reasoning and basic information-processing abilities of adolescents are comparable to those of adults, and thus “the factors that lead adolescents to engage in risky activity are social and emotional, not cognitive.” Although the decrease in risk-taking from adolescence to adults is attributable to maturation in the cognitive control system, according to Steinberg, the earlier maturing “socio-emotional system” leads to increased reward seeking (and, hence, risk taking) in adolescence. Relatively little research has been conducted on reasoning and information processing in adolescents, but the research that has been done suggests that the underlying competence to reason logically or probabilistically is present as early as elementary school, but is not necessarily tapped in decision making even by adults ( Reyna & Brainerd, 1994 ). Steinberg, then, focuses on the key question: What factors interfere with the ability to express that competence, especially in adolescence? Like Gerrard et al. (2008) and Casey et al. (2008) , Steinberg points to a “socio-emotional system that leads to increased reward seeking, especially in the presence of peers.”

A particularly dramatic example of peer effects on risk taking is provided by results of a study on simulated driving conducted with adolescents (mean age 14), youths (mean age 20), and adults (mean age 34). Subjects performed the driving task alone or in the presence of friends ( Gardner & Steinberg, 2005 ). In the task, a yellow traffic light signals that a wall will appear and the car will crash. The longer that subjects drive, the more points they get, but they also run the risk of crashing into the wall. The mere presence of friends “doubled risk-taking among the adolescents, increased it by fifty percent among the youths, but had no effect on the adults.” As Steinberg (2008) discusses, recent research with adolescents shows that social stimuli, such as peer acceptance (relative to rejection), activate brain areas known to be sensitive to reward. A large study of respondents ranging from 10 to 30 years old (N=935) confirmed that measures reflecting sensation-seeking and reward sensitivity increased from mid-childhood (age 10) until mid-adolescence (age 13 to 16). Tantalizing pilot data suggest that the presence of peers in the simulated driving task also activates reward circuitry. Such results are interpreted as showing that peers may make risk taking more rewarding. As Steinberg concludes, “In adolescence, then, more might not only be merrier – more may also be riskier.”

The mechanisms underlying social rewards in the brain are not entirely understood but Steinberg (2008) provides a cogent description of the working of the dopaminergic system. As Steinberg states, “dopamine plays a critical role in the brain's reward circuitry.” Therefore, remodeling of the dopaminergic system at puberty, and subtle changes in the number or relative density of dopamine receptors in cortical and subcortical areas of the brain, are plausibly implicated in changes in responsiveness to rewards during adolescence. Steinberg also provides an extremely thoughtful discussion of diverging views as to whether adolescents pursue rewards because they experience stimuli as less rewarding (the “reward deficiency syndrome”) or as more rewarding, relative to children and adults. Steinberg points out that adolescents do not consistently show more limbic activity when exposed to emotional stimuli than adults. Instead, it is the coordination (through improved connectivity) between cortical and subcortical limbic regions—the dance between affect and thinking--that may develop ( Finucane, Peters, & Slovic, 2003 ; see also Rivers et al., below).

Fuzzy-trace Theory

Many dual-process approaches assume that adolescents take risks not because they decide to do so, but, instead, because they react rather than decide. As we have seen, this view is variously enshrined in theory as the social reactivity path ( Gerrard et al., 2008 ), the socio-emotional system ( Steinberg, 2008 ), and the subcortical limbic system (which includes connected brain areas; Casey et al, 2008 ). Fuzzy-trace theory similarly assumes that reactivity decreases from childhood through adulthood, and that inhibition correspondingly increases ( Reyna & Mills, 2007 ; Rivers et al., 2008 ). However, according to this theory, the “other” dual process that opposes reactivity (or inhibition) is not solely analytical. (Fuzzy-trace theory remains a dual-process theory of reasoning because there are two qualitatively different reasoning modes; inhibition is not a reasoning mode but operates to withhold thoughts and actions.) In addition to a “verbatim-based” (focusing on precise literal details of information or experience) analytical mode of risky decision making, a gist-based intuitive mode is assumed. This gist-based intuitive mode operates on simple, bottom-line representations of the meaning of information or experience (see Reyna & Brainerd, 1995 ; Rivers et al., 2008 ). In this article, Rivers et al. describe how emotion interacts with different modes of thinking to produce risk taking in adolescence, reviewing research on emotion conceived as valence (positive-negative), arousal (excited-calm), feeling states (moods), and discrete emotions (e.g., anger vs. sadness).

Rivers et al. (2008) review the tenets of fuzzy-trace theory, which have been supported by empirical tests, including tests of mathematical models used to separately estimate gist-based, verbatim-based, and inhibitory processes. Fuzzy-trace theory is consistent with findings from a recent review of the existing literature on real-life risk taking in adolescence ( Reyna & Farley, 2006 ; see also Romer, 2003), but it has also led to new predictions and findings concerning adolescent risk taking that are discussed. A key finding is that risk taking in the laboratory and in real life has been found to often be analytical and intentional, that it involves an analytical process of weighing magnitudes of risks and benefits, and trading them off against one another. Thus, adolescents' conscious, reflective ratings of personal perceptions of risks and benefits often predict their behavior (see Reyna & Farley, 2006 ). Although risk takers might regret negative outcomes, they do not necessarily recant their perceptions of risks and benefits, which provide the calculus for their decisions. According to traditional economic theories, these decisions could be viewed as “rational” inasmuch as adolescents are pursuing their goals in accordance with their beliefs and values. However, according to fuzzy-trace theory, this kind of intentional, calculated risk taking is supplanted in mature adults by a simpler meaning-based approach that involves getting the core “gist” of important decisions, which allows adults to avoid unhealthy risks. Experiments on risky decision making have demonstrated that adults' behavior can be explained by specific gist-based processing and that younger adolescents' behavior can be explained by specific verbatim-based processing (e.g., Mills et al., in press ; Reyna, 1996 ; Reyna & Ellis, 1994 ).

As Rivers et al. (2008) discuss, strong emotions permeate adolescent risk taking. A central conclusion to emerge from this review is that gist representations frequently incorporate emotion (or affect), coloring the perception of risks and benefits and, hence, determining risk taking. Research has long shown that valence is encoded automatically and persists over time in memory, hallmarks of gist representations ( Osgood, Suci, & Tannebaum, 1957 ; Zajonc, 1980 ). Valence, derived from experience, supplies intuitions that protect adults from harm (e.g., Bechara, Damasio, Tranel, & Damasio, 2005 ). For example, as a result of social and cultural exposure, many adolescents derive the “valenced knowledge” that unsupervised parties are “fun” and are likely to encode them positively when faced with a decision (similar to images in prototype-willingness theory; see Figure 1 in Rivers et al.). Young children lack the experience to know much about what an unsupervised party entails, engendering a neutral reaction. Adults, however, “perceive readily the unsupervised party to be risky as negatively valenced knowledge is conjured up automatically, quickly likening the behavior to other obvious risks (such as driving drunk or having unprotected sex).” There is an abundant literature on valence (or affect) the details of which support interpretation in terms of gist representations (see also Reyna & Brainerd, in press ).

Rivers et al. (2008) also review research on mood congruency and other affect-as-information results, memory and emotion, reliance on gist-based stereotypes and heuristics, and the relation between arousal and inhibition. This research indicates that emotions conceived as valence, arousal, feeling states, or discrete emotions infiltrate the decision process in different ways. Emotions interfere with adolescents' ability to recognize the gist that danger is present; to reliably retrieve their values and principles that would protect them against unhealthy risk taking; and to reason “above the fray” of strong emotions using fragile, newly acquired gist representations rather than competing low-level, verbatim surface details (e.g., the irrelevant detail that the teens at an unsupervised party have never gotten in trouble before). Emotions also warrant gist interpretations of decision situations and pre-load responses to risk (e.g., anger encouraging risk taking and fear discouraging it) regardless of the verbatim facts of such situations ( Lerner & Keltner, 2001 ). Emotions bias information processing to focus either on those gist interpretations or on the verbatim facts. In short, “a full account of risk taking must encompass the role of emotion, in particular, the mechanisms through which it affects decision making.” According to fuzzy-trace theory, analysis or cold cognition is not the only alternative to reactive, impulsive processing: Gist-based intuition has been used to explain and predict risk taking in children, adolescents, and adults—and to design interventions to reduce unhealthy behaviors ( Reyna, in press ; Rivers et al.). Emotion is an important factor that defines, guides, and, at times, disrupts that gist-based intuition.

Conclusions: Settled Issues and Open Questions

The authors of the articles in this special issue on Current Theories of Risk and Rational Decision Making agree on a number of fundamental issues. First, they agree that adolescent risk taking is a crucially important health and public policy issue, and they each provide disturbing statistics to support this view. Sunstein (2008), a leading scholar of public policy, reinforces that point (and suggests “tools that policymakers might use if they seek to move adolescents in better directions”). Despite the seriousness and pervasiveness of this problem, it has only recently begun to attract a concerted intellectual effort. To be sure, there are longstanding efforts to describe the extent of the problem, as exemplified by the Youth Risk Behavior Survey (part of the Youth Risk Behavior Surveillance System of the Centers for Disease Control and Prevention) and other similar instruments. Recently, the MacArthur Foundation Research Network on Adolescent Development and Juvenile Justice launched an admirable effort to build a foundation of knowledge relevant to juvenile justice—but the problems of adolescent risk taking far outstrip the confines of the legal system. Medicine, education, transportation, and mental health are among the areas in which adolescent risk taking exacts an enormous toll in economic costs and human lives. However, research that focuses on causal mechanisms of adolescent risk taking, and that integrates such research with neurobiology or with rigorous theories of adult judgment and decision making, has been rare. Such research is essential, in our view, to make the scientific advances that will break the causal chain that produces adolescent mortality and morbidity.

The articles in this issue are an excellent first wave in what we hope will be a flood of theoretically motivated research on adolescent risk taking. This work is more than a proof-of-concept that deep theoretical work can be done on this important practical problem; the research programs represented in these articles are models of the kind of research that is needed. We have also argued that their scientific significance goes beyond adolescence. The influence of theories of adolescent risk taking and theories of adult judgment and decision making ought to be reciprocal in order to avoid serious gaps in scholarship and, ultimately, irrelevance regarding a large domain of real-life risk taking.

These articles also illustrate the kind of integrative approaches that are rapidly becoming standard science. Perhaps that is no where better illustrated than the resonant concept of “social meaning” discussed by Sunstein (2008), described as the “social signals that are sent by their [adolescents'] behavior,” which “varies across persons, groups, and time.” Social meaning captures bits of each of the approaches in this issue, from the socio-emotional system to the brain's responsiveness to rewards (which can sometimes be socially determined). Sunstein reminds us that social meaning is malleable, that even primary reinforcers, such as sex and hunger, are shaped by social context and interpretation, and images and gist all the more so.

Sunstein (2008) also draws our attention to some diversity of opinion concerning the effectiveness of behavioral interventions: As Sunstein notes, “Steinberg is not surprised that educational programs often have so little effect in reducing adolescent risk-taking.” In Steinberg's (2008) view, adolescent risk taking “is likely to be normative, biologically driven, and, to some extent, inevitable.” Casey et al. (2008) do not explicitly declare such a pessimistic view, but they, too, emphasize biological maturation. Very different perspectives are held by Fischhoff (2008) , Gerrard et al. (2008) , and Rivers et al. (2008) , each of whom is actively engaged in behavioral interventions. It goes without saying that there are many open questions that pertain to effective interventions, including the possibility that behavioral interventions might affect biological maturation and that biological factors might affect receptivity to behavioral interventions.

Finally, these approaches also differ with respect to their emphasis on prescription, and on whether characterizing rationality falls in the purview of the theory. Fischhoff's (2008) behavioral decision making framework takes an explicit approach to rationality, applying the triumvirate of descriptive, prescriptive, and normative considerations and harkening back to the axioms of subjective expected utility theory as the ultimate arbiter of rationality. Rivers et al. (2008) take a somewhat more empirically oriented view of rationality, appealing to evidence about developmental precedence: what develops earlier vs. what develops later, after considerable practice at a task (although both coherence, logical consistency, and correspondence, good outcomes, of decisions figure in the larger theory). The behavioral decision making framework and fuzzy-trace theory seem to take differing positions on whether “rationally” weighing costs and benefits (and trading them off quantitatively) is better or worse, overall, for adolescent risk taking (e.g., compared to processing the core gist of a decision). Although Gerrard et al. (2008) operate within the expectancy-value framework, similar to Fischhoff, they focus on the reduction of very real harms, such as those due to smoking. Both Steinberg (2008) and Casey et al. (2008) invoke evolutionary arguments about how aspects of biological maturation might have adaptive value. Despite its notorious subtlety, the issue of which decisions are good or bad, and how to tell, is one that we must continue to grapple with if research on adolescent rationality is to be relevant to public policy.

Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Contributor Information

Valerie F. Reyna, Departments of Human Development and Psychology; Center for Behavioral Economics and Decision Research, Cornell University.

Susan E. Rivers, Department of Psychology, Yale University and Department of Human Development, Cornell University.

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The Craft of Writing a Strong Hypothesis

Table of Contents

Writing a hypothesis is one of the essential elements of a scientific research paper. It needs to be to the point, clearly communicating what your research is trying to accomplish. A blurry, drawn-out, or complexly-structured hypothesis can confuse your readers. Or worse, the editor and peer reviewers.

A captivating hypothesis is not too intricate. This blog will take you through the process so that, by the end of it, you have a better idea of how to convey your research paper's intent in just one sentence.

What is a Hypothesis?

The first step in your scientific endeavor, a hypothesis, is a strong, concise statement that forms the basis of your research. It is not the same as a thesis statement , which is a brief summary of your research paper .

The sole purpose of a hypothesis is to predict your paper's findings, data, and conclusion. It comes from a place of curiosity and intuition . When you write a hypothesis, you're essentially making an educated guess based on scientific prejudices and evidence, which is further proven or disproven through the scientific method.

The reason for undertaking research is to observe a specific phenomenon. A hypothesis, therefore, lays out what the said phenomenon is. And it does so through two variables, an independent and dependent variable.

The independent variable is the cause behind the observation, while the dependent variable is the effect of the cause. A good example of this is “mixing red and blue forms purple.” In this hypothesis, mixing red and blue is the independent variable as you're combining the two colors at your own will. The formation of purple is the dependent variable as, in this case, it is conditional to the independent variable.

Different Types of Hypotheses‌

Types of hypotheses

Some would stand by the notion that there are only two types of hypotheses: a Null hypothesis and an Alternative hypothesis. While that may have some truth to it, it would be better to fully distinguish the most common forms as these terms come up so often, which might leave you out of context.

Apart from Null and Alternative, there are Complex, Simple, Directional, Non-Directional, Statistical, and Associative and casual hypotheses. They don't necessarily have to be exclusive, as one hypothesis can tick many boxes, but knowing the distinctions between them will make it easier for you to construct your own.

1. Null hypothesis

A null hypothesis proposes no relationship between two variables. Denoted by H 0 , it is a negative statement like “Attending physiotherapy sessions does not affect athletes' on-field performance.” Here, the author claims physiotherapy sessions have no effect on on-field performances. Even if there is, it's only a coincidence.

2. Alternative hypothesis

Considered to be the opposite of a null hypothesis, an alternative hypothesis is donated as H1 or Ha. It explicitly states that the dependent variable affects the independent variable. A good  alternative hypothesis example is “Attending physiotherapy sessions improves athletes' on-field performance.” or “Water evaporates at 100 °C. ” The alternative hypothesis further branches into directional and non-directional.

• Directional hypothesis: A hypothesis that states the result would be either positive or negative is called directional hypothesis. It accompanies H1 with either the ‘<' or ‘>' sign.
• Non-directional hypothesis: A non-directional hypothesis only claims an effect on the dependent variable. It does not clarify whether the result would be positive or negative. The sign for a non-directional hypothesis is ‘≠.'

3. Simple hypothesis

A simple hypothesis is a statement made to reflect the relation between exactly two variables. One independent and one dependent. Consider the example, “Smoking is a prominent cause of lung cancer." The dependent variable, lung cancer, is dependent on the independent variable, smoking.

4. Complex hypothesis

In contrast to a simple hypothesis, a complex hypothesis implies the relationship between multiple independent and dependent variables. For instance, “Individuals who eat more fruits tend to have higher immunity, lesser cholesterol, and high metabolism.” The independent variable is eating more fruits, while the dependent variables are higher immunity, lesser cholesterol, and high metabolism.

5. Associative and casual hypothesis

Associative and casual hypotheses don't exhibit how many variables there will be. They define the relationship between the variables. In an associative hypothesis, changing any one variable, dependent or independent, affects others. In a casual hypothesis, the independent variable directly affects the dependent.

6. Empirical hypothesis

Also referred to as the working hypothesis, an empirical hypothesis claims a theory's validation via experiments and observation. This way, the statement appears justifiable and different from a wild guess.

Say, the hypothesis is “Women who take iron tablets face a lesser risk of anemia than those who take vitamin B12.” This is an example of an empirical hypothesis where the researcher  the statement after assessing a group of women who take iron tablets and charting the findings.

7. Statistical hypothesis

The point of a statistical hypothesis is to test an already existing hypothesis by studying a population sample. Hypothesis like “44% of the Indian population belong in the age group of 22-27.” leverage evidence to prove or disprove a particular statement.

Characteristics of a Good Hypothesis

Writing a hypothesis is essential as it can make or break your research for you. That includes your chances of getting published in a journal. So when you're designing one, keep an eye out for these pointers:

• A research hypothesis has to be simple yet clear to look justifiable enough.
• It has to be testable — your research would be rendered pointless if too far-fetched into reality or limited by technology.
• It has to be precise about the results —what you are trying to do and achieve through it should come out in your hypothesis.
• A research hypothesis should be self-explanatory, leaving no doubt in the reader's mind.
• If you are developing a relational hypothesis, you need to include the variables and establish an appropriate relationship among them.
• A hypothesis must keep and reflect the scope for further investigations and experiments.

Separating a Hypothesis from a Prediction

Outside of academia, hypothesis and prediction are often used interchangeably. In research writing, this is not only confusing but also incorrect. And although a hypothesis and prediction are guesses at their core, there are many differences between them.

A hypothesis is an educated guess or even a testable prediction validated through research. It aims to analyze the gathered evidence and facts to define a relationship between variables and put forth a logical explanation behind the nature of events.

Predictions are assumptions or expected outcomes made without any backing evidence. They are more fictionally inclined regardless of where they originate from.

For this reason, a hypothesis holds much more weight than a prediction. It sticks to the scientific method rather than pure guesswork. "Planets revolve around the Sun." is an example of a hypothesis as it is previous knowledge and observed trends. Additionally, we can test it through the scientific method.

Whereas "COVID-19 will be eradicated by 2030." is a prediction. Even though it results from past trends, we can't prove or disprove it. So, the only way this gets validated is to wait and watch if COVID-19 cases end by 2030.

Finally, How to Write a Hypothesis

Quick tips on writing a hypothesis

1.  Be clear about your research question

A hypothesis should instantly address the research question or the problem statement. To do so, you need to ask a question. Understand the constraints of your undertaken research topic and then formulate a simple and topic-centric problem. Only after that can you develop a hypothesis and further test for evidence.

2. Carry out a recce

Once you have your research's foundation laid out, it would be best to conduct preliminary research. Go through previous theories, academic papers, data, and experiments before you start curating your research hypothesis. It will give you an idea of your hypothesis's viability or originality.

Making use of references from relevant research papers helps draft a good research hypothesis. SciSpace Discover offers a repository of over 270 million research papers to browse through and gain a deeper understanding of related studies on a particular topic. Additionally, you can use SciSpace Copilot , your AI research assistant, for reading any lengthy research paper and getting a more summarized context of it. A hypothesis can be formed after evaluating many such summarized research papers. Copilot also offers explanations for theories and equations, explains paper in simplified version, allows you to highlight any text in the paper or clip math equations and tables and provides a deeper, clear understanding of what is being said. This can improve the hypothesis by helping you identify potential research gaps.

3. Create a 3-dimensional hypothesis

Variables are an essential part of any reasonable hypothesis. So, identify your independent and dependent variable(s) and form a correlation between them. The ideal way to do this is to write the hypothetical assumption in the ‘if-then' form. If you use this form, make sure that you state the predefined relationship between the variables.

In another way, you can choose to present your hypothesis as a comparison between two variables. Here, you must specify the difference you expect to observe in the results.

4. Write the first draft

Now that everything is in place, it's time to write your hypothesis. For starters, create the first draft. In this version, write what you expect to find from your research.

Clearly separate your independent and dependent variables and the link between them. Don't fixate on syntax at this stage. The goal is to ensure your hypothesis addresses the issue.

5. Proof your hypothesis

After preparing the first draft of your hypothesis, you need to inspect it thoroughly. It should tick all the boxes, like being concise, straightforward, relevant, and accurate. Your final hypothesis has to be well-structured as well.

Research projects are an exciting and crucial part of being a scholar. And once you have your research question, you need a great hypothesis to begin conducting research. Thus, knowing how to write a hypothesis is very important.

Now that you have a firmer grasp on what a good hypothesis constitutes, the different kinds there are, and what process to follow, you will find it much easier to write your hypothesis, which ultimately helps your research.

Now it's easier than ever to streamline your research workflow with SciSpace Discover . Its integrated, comprehensive end-to-end platform for research allows scholars to easily discover, write and publish their research and fosters collaboration.

It includes everything you need, including a repository of over 270 million research papers across disciplines, SEO-optimized summaries and public profiles to show your expertise and experience.

If you found these tips on writing a research hypothesis useful, head over to our blog on Statistical Hypothesis Testing to learn about the top researchers, papers, and institutions in this domain.

Frequently Asked Questions (FAQs)

1. what is the definition of hypothesis.

According to the Oxford dictionary, a hypothesis is defined as “An idea or explanation of something that is based on a few known facts, but that has not yet been proved to be true or correct”.

2. What is an example of hypothesis?

The hypothesis is a statement that proposes a relationship between two or more variables. An example: "If we increase the number of new users who join our platform by 25%, then we will see an increase in revenue."

3. What is an example of null hypothesis?

A null hypothesis is a statement that there is no relationship between two variables. The null hypothesis is written as H0. The null hypothesis states that there is no effect. For example, if you're studying whether or not a particular type of exercise increases strength, your null hypothesis will be "there is no difference in strength between people who exercise and people who don't."

4. What are the types of research?

• Fundamental research

• Applied research

• Qualitative research

• Quantitative research

• Mixed research

• Exploratory research

• Longitudinal research

• Cross-sectional research

• Field research

• Laboratory research

• Fixed research

• Flexible research

• Action research

• Policy research

• Classification research

• Comparative research

• Causal research

• Inductive research

• Deductive research

5. How to write a hypothesis?

• Your hypothesis should be able to predict the relationship and outcome.

• Avoid wordiness by keeping it simple and brief.

• Your hypothesis should contain observable and testable outcomes.

• Your hypothesis should be relevant to the research question.

6. What are the 2 types of hypothesis?

• Null hypotheses are used to test the claim that "there is no difference between two groups of data".

• Alternative hypotheses test the claim that "there is a difference between two data groups".

7. Difference between research question and research hypothesis?

A research question is a broad, open-ended question you will try to answer through your research. A hypothesis is a statement based on prior research or theory that you expect to be true due to your study. Example - Research question: What are the factors that influence the adoption of the new technology? Research hypothesis: There is a positive relationship between age, education and income level with the adoption of the new technology.

8. What is plural for hypothesis?

The plural of hypothesis is hypotheses. Here's an example of how it would be used in a statement, "Numerous well-considered hypotheses are presented in this part, and they are supported by tables and figures that are well-illustrated."

9. What is the red queen hypothesis?

The red queen hypothesis in evolutionary biology states that species must constantly evolve to avoid extinction because if they don't, they will be outcompeted by other species that are evolving. Leigh Van Valen first proposed it in 1973; since then, it has been tested and substantiated many times.

10. Who is known as the father of null hypothesis?

The father of the null hypothesis is Sir Ronald Fisher. He published a paper in 1925 that introduced the concept of null hypothesis testing, and he was also the first to use the term itself.

11. When to reject null hypothesis?

You need to find a significant difference between your two populations to reject the null hypothesis. You can determine that by running statistical tests such as an independent sample t-test or a dependent sample t-test. You should reject the null hypothesis if the p-value is less than 0.05.

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MASTER'S THESIS Title of thesis: Value of Risk Management Credits (ECTS): 30

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Exploring the indirect links between enterprise risk management and the financial performance of SMEs

• Original Article
• Published: 12 December 2022
• Volume 25 , article number  1 , ( 2023 )

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• Lenka Syrová   ORCID: orcid.org/0000-0003-1401-9784 1 &
• Jindřich Špička   ORCID: orcid.org/0000-0001-5699-9544 1  

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This paper responds to the lack of empirical evidence on how enterprise risk management (ERM) and the financial performance of small and medium-sized enterprises (SMEs) are related. Structural equation modeling is used to explore new mediators in the relationship between ERM and SME financial performance. The results show that organizational culture (mission dimension) and strategic risk management performance are full and positive mediators between ERM and financial performance. These research results highlight the fact that the implementation of ERM in an enterprise does not by itself generate the expected effects without the existence of a mature organizational culture and the monitoring of strategic risk management performance. These findings are particularly relevant for SMEs with “pretend ERM” that lacks the strategic and operational components. ERM also helps to transform the negative effect of foreign capital in SME equity on financial performance into a positive effect.

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Introduction

Increasing levels of uncertainty call for proactive risk management in all organizations. The parallel crises triggered by the COVID-19 pandemic (Chakraborty and Maity 2020 ) and the military conflict in Ukraine have impacted most industries and businesses, unlike the Great Recession of the late 2000s, which primarily affected the financial sector (Gertler and Gilchrist 2018 ). Systematic risk has long been underestimated in advanced economies (Pagach and Wieczorek-Kosmala 2020 ). In such a situation, an intuitive assessment of risk outcomes, as often performed by smaller enterprises, is not enough (Grondys et al. 2021 ). Companies face new challenges and find it harder to maintain their profitability and competitiveness. Therefore, holistic enterprise risk management (ERM) is becoming increasingly important in small and medium-sized enterprises (SMEs).

Nonfinancial SMEs are mostly unregulated. Thus, there is little pressure to implement a comprehensive risk management system. Nevertheless, in recent years, SMEs have started implementing formal risk management processes to increase their competitiveness (Wirahadi and Pasaribu 2022 ). ERM improves the quality of the information about enterprise risk profiles. The adoption of ERM reduces systematic risk. The purpose of ERM is to reduce the probability of losses and, therefore, reduce the need to borrow external resources, which positively impacts the expected cost of capital (Berry-Stölzle and Xu 2018 ).

The implementation of a risk management system entails many internal changes. International risk management standard ISO 31000 provides principles, frameworks, and procedures for risk management regardless of the size and orientation of the organization (Aven 2017 ). The Committee of Sponsoring Organizations of the Treadway Commission (COSO) provides an alternative ERM framework. Such strategic changes are financially and organizationally challenging and sometimes take several years to implement. The difficulty of implementing a holistic risk management system such as ERM may not be as great for large and capital-intensive companies. Nevertheless, the organizational integration of ERM can take a long time given the complexity of the organizational structure of large companies. On the other hand, SMEs usually do not have as high of a capital capacity for implementing ERM, but organizational integration may be faster due to the greater flexibility of SME decision-making (Adomako et al. 2021 ).

SMEs are a vulnerable group of companies because they may lack the resources necessary to overcome a crisis (Rathore and Khanna 2020 ). At the same time, the high volatility of the economic environment exacerbates the uncertainty and unpredictability of economic factors, increasing the risk associated with doing business (Gengatharan et al. 2020 ). In addition, the size of the business influences the amount of risk taken, which is generally lower for larger companies (Jenny 2020 ). Moreover, SMEs are a vital part of the European economy. The average value contributed by SMEs to the economy in the European Union is approximately 56% (Statista 2021 ).

Most research on ERM has been conducted empirically in large financial and publicly traded companies in emerging markets (Florio and Leoni 2017 ). SMEs are largely unregulated, and there is no intense pressure to implement a holistic risk management system. However, SMEs are now in a more difficult situation. ERM is a way for SMEs to proactively manage their business risks while improving their business performance, as confirmed among large enterprises (Syrová and Špička 2022b ). The research gap lies in the unanswered question of whether the implementation of ERM improves the financial performance of SMEs.

This article responds to the ongoing crisis and changes in the business environment. The authors emphasize the growing need to study the impact of the ERM approach among SMEs. ERM can significantly contribute to the maintenance of company competitiveness and crisis survival. This research results in the development of a new model that extends the theoretical understanding of ERM in SMEs. The study reveals significant mediators that positively influence the relationship between ERM and firm financial performance. The findings provide a critical understanding of the role of ERM in SMEs and the realization that the ERM approach is not self-sustaining. Simply implementing an ERM approach does not directly impact SME performance.

This research focuses on the implementation of ERM in Czech SMEs. The Czech Republic is a Central European country, and most Czech SMEs were established in the early 1990s after forty years under the centrally planned socialist economy. The Czech Republic is an open and export-oriented economy in which services and industry play a dominant role. It has been operating in the European Union’s single market since 2004. The contribution of SMEs to GDP is approximately 40%, below the EU average, and SME exports account for more than half of all Czech exports (Bures 2017 ). The management of SMEs in the Czech Republic was affected by the loss of business continuity. An integral part of the transformation into a postsocialist economy was the incorporation of risk into management decisions in the 1990s. Research from neighboring Slovakia shows that risk management was conducted in a relatively intuitive manner, without data support or the appropriate methods, know-how, and trained staff to make management decisions (Klučka and Grünbichler 2020 ). The study by Virglerova ( 2019 ) points out the lack of financial risk management experts.

This paper explores the relationship between ERM and subjective financial performance among nonfinancial SMEs in the Czech Republic. To achieve this goal, the study quantifies the mediating effects of organizational culture and strategic risk management performance and recapitulates the previously revealed mediators of this relationship. The main contribution of the paper lies in the development of a new model for studying the impact of ERM on the subjective financial performance of SMEs. The results show that organizational culture (mission dimension) is a catalyst for ERM effects, while at the same time, the implementation of an ERM performance monitoring system improves the subjective financial performance of the enterprise. The originality of the paper is in showing that ERM is not self-sustaining. ERM does not spill over to all levels of management nor have desirable effects on the strategic financial objectives of the SME without a strong organizational culture and a good performance monitoring system.

Theoretical foundation

The goal of risk management is to minimize key risks, and an appropriate level of risk management that enhances value for owners and other stakeholders must be chosen (Meulbroek 2002 ). The ERM approach focuses on all potential future risks (both pure and speculative) (Schiller and Prpich 2014 ). Enterprises can focus on risk management opportunities by incorporating the dual nature of speculative risks (Lundqvist 2015 ).

The ERM approach should, among other things, explicitly identify the threats to firm value and the opportunities to increase it (Gatzert and Martin 2015 ). The findings of a systematic literature review (Syrová and Špička 2022b ) show that the relationship between ERM and company performance is not direct but is mediated by strategic agility (Ai Ping et al. 2017 ), competitive advantage (Yang et al. 2018 ), strategic planning (Sax and Andersen 2019 ), and information systems quality (Kurdi et al. 2019 ). Previous research has mainly been conducted in listed companies and large international firms (Callahan and Soileau 2017 ; Farrell and Gallagher 2019 ; Kommunuri et al. 2016 ; Laisasikorn and Rompho 2014 ; Malik et al. 2020 ; Quon et al. 2012 ). Only a few studies have focused on SMEs. The results of the recent research studies show mostly positive relationship between ERM and SME performance (Hanggraeni et al. 2019 ; Jenya and Sandada 2017 ; Rehman and Anwar 2019 ; Yang et al. 2018 ). However, the results of some studies on SMEs identified the relationship between ERM and performance as insignificant (Glowka et al. 2020 ; Hiebl et al. 2019 ). Other studies quantified the relationship ambiguously depending on the analysis of the individual components of ERM (Heong and Teng 2018 ; Yakob 2019). The authors of the studies conducted in SMEs mainly used subjective assessment of firm performance and multiple regression analysis.

The purpose of ERM is to integrate risks into the enterprise’s organizational design and decision-making process (Ogutu et al. 2018 ). Given that ERM is a critical initiative that helps increase organizational resiliency in times of uncertainty, it is reasonable to assume that the internal culture of the firm is a significant factor in ERM adoption. Indeed, ERM adopters encounter issues related to organizational culture, but the mediating effect of organizational culture on the relationship between ERM and organizational financial performance has not yet been empirically evaluated and demonstrated.

• Organizational culture

Organizational culture is the set of the underlying values, beliefs, and assumptions within an organization, the patterns of behavior that result from those perspectives, and the symbols that express the connections among the assumptions, values, and behaviors of organizational members (Denison 1990 ). Several empirical studies have demonstrated the positive impact of organizational culture on organizational performance (Han 2012 ; Tadevosyanová 2015 ; Bhuiyan et al. 2020 ). However, the effect of organizational culture on the effectiveness of ERM implementation has not yet been demonstrated. Organizational culture enables more effortless penetration of ERM into all functional areas of the organization and faster adaptation under the conditions of risk and uncertainty (Thomya and Saenchaiyathon 2015 ).

There are different types of organizational culture: market culture, clan culture, adhocratic culture, and hierarchical culture (Cameron and Quinn 2011 ). Research has shown that only clan cultures positively affect project performance and internal and external organizational performance. In contrast, hierarchical cultures, market cultures, and adhocratic cultures do not affect organizational performance (Yazici 2011 ). However, the same research (Yazici 2011 ) also showed that managerial experience enhances the positive influence of clan culture (on project performance), adhocratic culture (on project performance and internal and external firm performance), and market culture (on external firm performance).

On the other hand, a hierarchical culture does not impact performance because it creates a hostile work environment by bureaucratizing the organizational structure. A hierarchical culture is characterized by a formalized and structured work environment emphasizing procedures and regulations whose unifying element is formal rules. Managers are expected to be good coordinators and organizers who can keep the organization running smoothly, consistently, and efficiently (Cameron and Quinn 2011 ).

Denison’s Organizational Culture Questionnaire is one of the most popular methods for operationalizing organizational culture (Denison 1990 ). A study by Denison and Mishra (Denison and Mishra 1995 ) found that all four dimensions of organizational culture—mission, consistency, commitment, and adaptability—were related to various performance criteria. Commitment and adaptability are indicators of flexibility, openness, and responsiveness and are strong drivers of organizational growth. Consistency and mission indicate organizational direction, integration, and vision and are good predictors of profitability. All four characteristics of organizational culture are essential predictors of quality, employee satisfaction, and overall performance. According to Denison, the strongest predictor of performance is the organization’s mission, i.e., whether the organization has an articulated mission and whether its employees share that mission. Denison’s scales for consistency (e.g., Do you have coordinated systems that allow you to build consensus based on your core values?) and mission (e.g., Do you know where you are going? Do you have clear goals and a strategy to achieve them?”) might be good indicators of organizational culture in the context of the relationship between ERM and financial performance.

Organizational culture (mission dimension) mediates the relationship between ERM and the subjective financial performance of SMEs.

Organizational culture (consistency dimension) mediates the relationship between ERM and the subjective financial performance of SMEs.

Through organizational culture, ERM is disseminated and cultivated throughout the organization. The overarching dimensions of organizational culture, namely, consistency and mission, could provide an appropriate implementation framework for ERM because organizational culture is a system of shared assumptions, attitudes, beliefs, habits, and values that form the basis for typical behavior patterns (Gordon 1991 ).

• Strategic risk management performance

Research in strategic risk management has highlighted the importance of creating a risk management culture at all levels of the organization (Moeller 2007 ). A risk management culture is defined as the shared values and beliefs of an organization’s employees (decision-makers) regarding risk-taking (Bui et al. 2018 ). Through their risk management culture, organizations are able to quickly identify and hedge key risks and respond to and mitigate unforeseen risks while identifying and capitalizing on new opportunities early on using an ERM approach to improve risk performance (Sax and Andersen 2019 ). A risk management culture is critical to an organization’s strategic decision-making and requires the active involvement of the board and senior management. Top management shapes risk culture through leadership, transparent communication, and risk management using appropriate processes and resources (Osman and Lew 2020 ).

While the impact of ERM and strategic reactivity has been tested in terms of firm performance and value, little is known about the impact of ERM on strategic risk performance (Sax and Torp 2015 ). Strategic risk management can be integrated into effective, well-known processes to bridge the gap between the risk and strategic management literatures. Risk management is not just the concern of the central risk management department. To create an effective risk management system, the enterprise must build a dynamic risk management team that quickly identifies and addresses new threats and opportunities. Thus, the risk management becomes strategic as it encompasses the culture and leadership styles and is reinforced by strategic responsiveness. Incorporating evaluations of strategic risk management performance as an integral part of governance could make ERM more effective in terms of the financial goals it seeks to achieve. Moreover, the 2017 update to the COSO framework emphasizes the importance of integrating ERM with business strategy and performance (COSO 2017 ).

Strategic risk management performance mediates the relationship between ERM and the subjective financial performance of SMEs.

Materials and methods

The level of ERM in a company can generally be determined through a questionnaire survey or a content analysis of company documents. Early empirical studies assessed the level of ERM with a binary approach, used primarily in content analysis (Silva et al. 2019 ). Content analysis can be used as a method to determine the presence of ERM by determining whether ERM is used (1 = the company uses ERM, or relevant keywords are listed in company documents) or not (0 = the company does not use ERM, or relevant keywords are not listed in company documents). However, a binary score alone cannot determine the extent of ERM implementation. For this reason, some authors have adopted an ordinal measure (Husainia et al. 2019 ; Darmastuti et al. 2020 ), with individual ERM metrics (obtained either from a content analysis or a questionnaire survey) summed together. The resulting summation yields the value of a simplified maturity index (Florio and Leoni 2017 ).

Moreover, the disclosure of risk management information in SME reporting is voluntary. For this reason, the authors of this study choose the quantitative questionnaire survey method. Through the questionnaire survey, it is possible to obtain primary data and more accurate information on the level of ERM implementation in a given company when secondary data in company reports are not available, as with SMEs.

The authors chose quantitative research because the vast majority of previous studies on the relationship between ERM and corporate financial performance have been based on quantitative research. Quantitative research is more objective than qualitative research, and the results are based on larger samples that are representative and generalizable to the population (in this case to SMEs in the Czech Republic). Quantitative research can provide accurate, reliable and consistent data that can be processed using validated statistical methods.

The sample covers nonfinancial SMEs in the Czech Republic. The targeted sample consists of 300 SMEs that are members of the Association of Small and Medium-sized Enterprises in the Czech Republic. The sample size provides sufficient statistical power for the tests. Quota sampling ensures the representativeness of the sample and the generalizability of the results although it is not based on random selection but on a predefined panel of firms willing to respond. Data were collected from September to November 2021 through the external research company Ipsos which closely cooperates with Association of Small and Medium-sized Enterprises in the Czech Republic. Respondents were owners, CEOs, senior managers, sales managers, and finance/commercial managers. These roles should have a sufficient level of responsibility to ensure the accuracy of the responses. Unlike large and multinational companies, SMEs do not typically employ a chief risk officer or risk manager, as risk management is the responsibility of the top management or the business owners. Response variability was calculated and unusual values were identified to clean the original sample of 300 SMEs, and a final sample of 296 respondents was obtained.

The self‐reporting is frequently applied for measuring the individual opinions and statements in the quantitative research. Unlike objective measures, which are not affected by personal bias and are represented by facts, the subjective self-reporting is associated with possible biases negatively affecting validity and reliability. Using self-reported information for decision-making results in endogenous selection bias which creates spurious associations between the measure being reported and factors that influence reporting (Scott and Balthrop 2021 ). However, self-reporting through the batteries of questions is the standard form of information-gathering mechanism for Structural Equation Modelling which effectively tests the relationship between latent variables (Hatcher 2013 ).

Independent variable (ERM)

The study uses an ordinally scaled ERM index incorporating the number of ERM characteristics. There are 14 characteristics, each taking on a binary value (1 if the company reports the presence of the characteristic, 0 if not). The ERM characteristics were adopted from Miloš Sprčić et al. ( 2017 ), who were inspired, for example, by COSO ( 2004 ), Lundqvist ( 2014 ), and Meulbroek ( 2002 ).

The ERM construct (Appendix 1) assumes that SMEs may not have formalized policies or internal regulations regarding risk management. The methodology used to assess the level of ERM has already been validated in empirical research in Central Europe, which has used the same terminology in its construction of the questions (Miloš Sprčić et al. 2017 ; Marc et al. 2018 ; Mardessi and Ben Arab 2018 ).

Dependent variable (subjective financial performance)

Subjective financial performance (Appendix 1) is measured using the validated construct developed by Uhlaner et al. ( 2014 ) and is based on three indicators: the financial performance of the company compared to its competitors (5-point scale from 1 = much worse to 5 = much better), profitability in the last fiscal year (7-point scale from 1 = extreme losses to 7 = extremely profitable in the last fiscal year), and current liquidity (4-point scale from 1 = very low liquidity to 4 = substantial liquidity). This subjective assessment of financial performance is not tied to companies’ financial statements, which are generally published only by medium-large and large companies (Kamboj and Rahman 2015 ; Abbasi and Weigand 2017 ; Kumar et al. 2018 ). In contrast, a subjective assessment of financial performance is appropriate for questionnaire surveys among SMEs.

Organizational culture is the hypothetical mediator of the relationship between ERM and the subjective financial performance of SMEs (Appendix 1). The construct of organizational culture is taken from Denison ( 1990 ). Only two dimensions (corporate mission and corporate consistency) are expected to relate to company performance and stability based on previous research (Tadevosyanová 2015 ). Answers to individual statements are given on a 5-point Likert scale (1 = strongly disagree to 5 = strongly agree).

Strategic risk management performance (SRMP) is another hypothetical mediator of the relationship between ERM and the subjective financial performance of SMEs (Appendix 3). The scales for strategic risk management performance were adopted from Sax and Torp ( 2015 ), where respondents were asked to make three comparisons with their competitors, considering the past three years, using a 7-point scale (from 1 = significantly worse to 7 = significantly better). Specifically, the comparisons are ‘Ability to hedge against key known risks and uncertainties’, ‘Ability to respond to and mitigate unforeseen risks’, and ‘Ability to seize new opportunities’.

Control variables

The ERM control variables are firm size as measured by the number of employees (Beasley et al. 2015 ; Gordon et al. 2009 ), firm age (Yang et al. 2018 ), and the proportion of foreign capital in the firm (Syrová and Špička 2022a ). Previous studies have shown that foreign direct investment has a positive effect on the ability to use advanced forms of technology, to employ managers with greater international experience and who are more skilled in using modern management techniques, to apply good corporate governance practices and to access credit in international financial markets (Abor 2010 ). SMEs may have limited opportunities for foreign investment compared to large firms. Another reason could be the historical context of post-communist countries, where fear of foreign investment or investors may still exist.

• Structural equation modeling

The method used to explore the relationship between ERM and the subjective financial performance of SMEs is structural equation modeling (SEM). This method has also been applied by other authors who have studied the effects of ERM, e.g., (Ai Ping and Muthuveloo 2015 ; Wisutteewong and Rompho 2015). SEM is a method of multivariate analysis used to test and estimate complex causal relationships among variables, even when those relationships are hypothetical or not directly observable (Williams et al. 2009 ). The authors selected SEM because ERM, subjective financial performance, and the proposed mediators cannot be measured directly with a simple question.

The main advantage of SEM is the more efficient evaluation of measurement and structural path models, mainly when the structural model contains multiple dependent variables and latent constructs based on proxy variables with multiple items (Astrachan et al. 2014 ). Compared to other statistical methods such as regression, SEM allows researchers to simultaneously assess the relationships between constructs with multiple items (latent variables) and reduces the overall error associated with the model. Another advantage over regression is the ability to conduct a path analysis for all structural relationships at once, which leads to more accurate results (Astrachan et al. 2014 ).

There are two basic types of SEM—covariance-based SEM (CB-SEM) and partial least squares SEM (PLS-SEM). CB-SEM is used mainly to confirm theories. To this end, it determines how well a proposed theoretical model can estimate the covariance matrix for a sample of data. In contrast, PLS-SEM is used mainly for theory development in exploratory research, as it explains the variance of the dependent variable when the model is examined (Hair et al. 2017 ). Although PLS-SEM is a regression method, it is nonparametric. That is, it makes no assumptions regarding the distribution of the data. PLS-SEM does not assume that the data are normally distributed; moreover, it is appropriate to use PLS-SEM when the data are categorical or ordinal or contain a single item (Hair et al. 2017 ). PLS-SEM does not assume that the proxies created are identical to the constructs (latent variables) that they replace. They are explicitly recognized as proxies (Hair et al. 2017 ). In this exploratory study, PLS-SEM and the bootstrapping method (5,000 iterations, path weighting scheme) are used to test the significance of the relationships in the model.

The structure of the sample is matched to that of the national economy to ensure the representativeness of the sample in terms of company size and sector (Table 1 ).

The authors use a formative measurement approach for the PLS-SEM analysis (see Appendix 2). The PLS-SEM contains the following:

Latent variables: ERM level (ERM), subjective financial performance of the company (FP), organizational culture–mission dimension (ORGM), organizational culture–consistency dimension (ORGC), and strategic risk management performance (SRMP).

Manifest variables: proportion of foreign capital in the company (FC), firm size (FS), and firm age (FA).

Table 2 contains basic description of the latent and manifest variables. Descriptive statistics of the latent variables were calculated from the mean scores of the partial manifest variables for each enterprise because of the relatively high reliability of the constructs.

The PLS-SEM analysis follows the steps recommended by Hair et al. ( 2017 ). The final model is iteratively explored (Fig.  1 ).

Source Authors’ own elaboration

Iterative exploration of the final model through PLS-SEM.

The proposed model with proxy variables shows a high discriminant validity (HTMT) value for the relationship between ORGC and ORGM (0.977). In addition, ORGC proved to be a nonsignificant mediator at a 5% significance level. Moreover, the internal variance inflation factor (VIF) between ORGC and ORGM is high (3.544). Therefore, organizational culture–consistency dimension (ORGC) was excluded from further modeling. The next step resulted in the identification of ORGM as a full mediator in the relationship between ERM level and strategic risk management performance (Zhao et al. 2010 ). Figure  2 presents the final model.

Source Own calculations

Final PLS-SEM model.

The final model satisfies the assumptions of a robust model (discriminant validity according to HTMT, collinearity, reliability). Appendix 3 presents the details.

The model results (Table 3 ) show that foreign capital share and firm size have a direct and positive effect on ERM level, while firm age has an inversely proportional effect on ERM level. Organizational culture–mission dimension is a significant mediator between ERM and subjective financial performance. The strategic risk management performance tracking system also plays an important role in the relationship between ERM and subjective financial performance. The standardized root mean square residual (SRMR) and the RMS theta indicate a well-fitting model (Table 4 ). The final model also includes the results for the indirect effects, which are discussed in the next section (Table 5 ).

This study identifies new significant variables that mediate the effect of ERM on the subjective financial performance of SMEs. The model includes the latent variables of ERM level (Miloš Sprčić et al. 2017 ), strategic risk management performance (Sax and Torp 2015 ), organizational culture→mission dimension (Denison 1990 ), and subjective financial performance (Uhlaner et al. 2014 )→and the determinants of ERM identified in previous studies: the proportion of foreign capital in the company, firm size, and firm age.

The results show that firm size directly affects the level of ERM in a given firm (0.178), which supports the findings of previous studies (Nasir 2018 ; Jurdi and AlGhnaimat 2021 ). As company size increases, there is a need to manage the company using formal procedures and internal guidelines. The need to manage the business increases, as does the need to manage risk formally. Small enterprises may lack the resources and reliable mechanisms needed to support their risk management activities (Brustbauer 2014 ). In addition, for small enterprises that are do not face regulatory pressure, full ERM implementation may not be necessary because the benefits of ERM do not outweigh the associated costs.

SMEs do not necessarily benefit from adopting formal ERM methods (Hiebl et al. 2019 ). Because a firm’s processes become more formalized as it grows, SMEs have a greater need for more efficient ERM techniques and, therefore, may be able to implement ERM because of a greater availability of resources. In addition, previous research has shown that companies that have implemented ERM perform better (Gordon et al. 2009 ; Grace et al. 2015 ), have higher value (Farrell and Gallagher 2015 ), and have a lower cost of capital (Berry-Stölzle and Xu 2018 ). Large companies’ business activities and transaction types are more diverse and complex than those of smaller companies (Witek-Crabb 2014 ). In addition, larger companies can devote more resources and capacity to more diversified alternative investments (Golshan and Rasid 2012 ).

Thus, growing companies that have not implemented ERM may be missing opportunities to improve their business performance and value. From a management perspective, it would be valuable to understand why some mid-sized companies have not implemented ERM or are hesitant about implementing ERM.

A reluctance to adopt ERM and the corresponding lack of benefits relate to firm age . The study results show that the age of the company has an inverse influence on the level of ERM (− 0.168). Younger companies are not encumbered by history, are more flexible, and are led by managers with better theoretical knowledge of modern management methods. The historical context of the Czech Republic is characterized by the disappearance of many SMEs due to the political regime and centrally planned economy. After the political regime changed in 1990, SMEs started to form again, but with a loss of continuity in their management styles (Tarko 2020 ). The older a company is, the less likely it is to use advanced ERM techniques. Older companies that have operated for a longer time tend to institutionalize existing processes and adopt bureaucratic behavior, leading to barriers to strategic change (Hannan and Freeman 1984 ), which can also negatively affect financial performance. Thus, firm age could harm ERM implementation, a finding that contrasts with the results of a study examining the relationship between firm age and innovation in the work environment, which shows that firm age has a positive effect (Dukeov et al. 2018 ). An explanation for the relationship between firm age and the level of ERM implementation can also be found in Greiner’s theoretical model of firm growth (Greiner 1989 ). Older companies may suffer from a bureaucratic crisis in which the company spends more and more time only on internal matters, leaving no time to implement new management practices, including ERM.

Our research has also explored the positive impact of foreign capital in SME equity on ERM levels (0.345), which is one of the important contributions of this paper.

The global business environment and internationalization are great challenges for companies that want to expand their business activities, but they also pose a risk if those companies’ business plans fail. Competition and constant changes in material costs, tax and insurance burdens, and growth in energy processes are the sources of many problems that can lead to a loss of market share and to financial losses (Hudáková and Masár 2018 ). However, most SMEs do not have to own a foreign subsidiary directly in order to participate in other international activities (Gubik and Bartha 2014 ), such as direct investments or other foreign equity investments. A study that examined the presence of foreign direct investment in SMEs found a positive relationship with SME development (Lu and Beamish 2006 ).

Many SMEs resist foreign investment and foreign capital. The arguments of the owners, which invoke national tradition, are not always beneficial for the company from a long-term strategic point of view and often express a hidden fear for their own career and the fear of losing control over their company. This is confirmed by the research findings of this paper: the share of foreign capital positively impacts the level of ERM (0.345). The inflow of foreign capital means a strengthening of capital and more control, which can be exploited precisely through ERM. Foreign investors can result in faster adoption of international standards such as ISO. However, the adoption rate does not depend on the amount of foreign investment but on the investor (Prakash and Potoski 2007 ). The Czech Republic receives investments mainly from Western European countries, where the ERM approach may be more widespread. Another argument supporting the positive impact of foreign capital on the level of ERM is the ability to adequately manage the increased risks associated with receiving foreign capital. A study conducted with a sample of African financial institutions supports the authors’ research findings. The results show that the presence of foreign capital significantly affects ERM implementation (Matovu 2017 ).

Implementing ERM alone does not result in improved business performance or other benefits. The implementation of formal ERM practices and processes must be supported by general agreements among employees and management. Organizational culture is a catalyst for the ERM approach. Our study also examines the ability of strategic risk management to connect all levels of management.

The PLS-SEM results support H1: Organizational culture (mission dimension) mediates the relationship between ERM and the subjective financial performance of SMEs. However, the proportion of foreign equity has an adverse effect on the organizational culture – mission dimension (− 0.179). This negative effect could be caused by different understandings of the mission from the investors’ point of view. With the fragmentation of investors, there may be fewer common goals in a given company. This negative impact may even affect firm performance (Foreign capital→ Organizational culture–mission→ Financial performance: indirect effect = − 0.038; Table 5 ). However, when a firm uses the ERM approach, the overall indirect effect of the proportion of foreign equity on the subjective financial performance of the firm is positive in the presence of the mediating variable ERM (Foreign capital→ ERM level→ Organizational culture–mission→ Financial performance: indirect effect = 0.013; Table 5 ). Thus, the level of ERM as a mediating variable can transform the negative effect of foreign equity on financial performance into a positive effect through the organizational culture (mission dimension). This result demonstrates the central role of ERM in organizations, which is consistent with previous studies (e.g., Baxter et al. 2013 ; Hoyt and Liebenberg 2011 ; Laisasikorn and Rompho 2014 ).

The results clearly show the inevitable and crucial role of ERM when companies decide to expand abroad or allow foreign investors. The ERM approach mitigates the negative impact of foreign capital on the consistency of organizational culture (mission dimension) and supports the financial performance of the company at the same time. According to previous studies, organizational culture itself positively affects firm performance (Han 2012 ; Tadevosyanová 2015 ; Bhuiyan et al. 2020 ). However, previous studies have not established a link between organizational culture, ERM and the business performance of SMEs.

The PLS-SEM results do not support H2; the variable organizational culture (consistency dimension) was removed from the model due to the high value of discriminant validity with organizational culture (mission dimension) and the concurrent insignificance of the relationship at the 5% significance level .

The results of the PLS-SEM analysis do not support Hypothesis H3: strategic risk management performance mediates the relationship between ERM and the subjective financial performance of SMEs. The ERM approach should be present at all management levels within the organization and should also positively influence the performance of strategic risk management. The relationship is indirect and is mediated through organizational culture (mission dimension). The mission dimension of organizational culture is strategic and positively supports the strategic risk management performance (0.356). However, the ERM approach should include strategic, operational, and control perspectives (Dvorski Lacković et al. 2022 ); moreover, COSO ( 2017 ) also includes the components of “strategy and objective-setting” and “performance”. The results may have been obtained because a relatively large proportion of companies (approximately 30%) use a version of ERM called “pretend ERM”, where the SMEs have formally implemented an ERM approach, but the risk management system lacks the strategic and operational components of an ERM system and focuses only on the reporting aspect (Dvorski Lacković et al. 2022 ; Syrová and Špička 2022a ).

Conclusion and implications

Regarding the theoretical implications, this study reveals new mediators between ERM and the subjective financial performance of SMEs. The PLS-SEM method is suitable for analyzing complex relationships and testing causal relationships. Exploring indirect pathways can reveal consequential effects and help managers and owners understand various relationships. Complicated ERM indices (e.g., Gordon et al. 2009 ) are not suitable for the nonfinancial sector because the input variables for calculating such indices are difficult or impossible to obtain. The model works with the direct and indirect effects of ERM implementation. The indirect effects show the crucial role of organizational culture (mission dimension) and evaluations of strategic risk management performance in the relationship between ERM and the subjective financial performance of SMEs.

From the management perspective, it is essential to establish functional and integrated processes for ERM implementation. ERM must be integrated with the organizational culture and the performance monitoring systems in the SME. Managers and owners should emphasize the functional implementation of ERM, not just a pretend ERM (Syrová and Špička 2022a ) that lacks all the elements of an ERM approach. The ERM system must not be a “facade without the substance” that does not contribute to better planning and decision-making processes (Dvorski Lacković et al. 2022 ).

This research provides new information about the role of foreign capital in nonfinancial SMEs—it is a determinant that has a positive impact on ERM implementation. The share of foreign capital results in an inflow of new management practices and process innovations and the transfer of international management techniques. At the same time, the contribution of foreign capital leads to a greater need for corporate control and integrated management of the risks associated with foreign investors or other foreign activities. Managers and owners need to monitor the impact of foreign capital on the company’s internal organization and organizational culture and subsequent changes. The share of foreign capital in equity can harm a company’s internal environment, which is consistent with the results of our research.

When deciding to use foreign capital for business development, it is important to control for the associated external risks (investment, credit, interest rate, and market risks) and for internal consistency and risks arising from the inclusion of other types of capital. The effect of foreign capital puts managers and owners in a difficult position. It is essential to focus on the internal consistency of the company, proper communication within the company, and the maintenance of consistency in the direction and vision of the company. It is recommended that ERM be implemented in nonfinancial SMEs because the level of ERM can transform the negative effect of foreign equity on financial performance into a positive effect through organizational culture (mission dimension). Thus, the study reveals that ERM plays a positive mediating role for SMEs.

The research findings provide new information on the level and impact of ERM in the Visegrad Four country. The findings on the use of foreign capital, facilitating the implementation of ERM even at the expense of deterioration of organizational culture—the mission dimension, is new information for owners/managers in SMEs. It is foreign capital that is one of the problem areas in post-communist countries. There is an area for further research outside of Central Europe to compare the role of foreign capital in SMEs. Further opportunities for research were identified by the authors in the area of Organizational Culture and its other dimensions, which were not examined in the study. The mediating variables were selected based on the literature review, but there are still a number of variables that need to be analyzed in more detail in the SME environment. Investigating the differences between family and non-family businesses in SME ERM could also provide interesting results, with the possibility of building on the findings by Glowka et al. ( 2020 ).

Another opportunity is to conduct qualitative research to identify the reasons that reflect the relatively high percentage of low levels of ERM implementation in SMEs. Quantitative research has shown that ERM has a positive impact on the subjective financial performance of the company. The authors see the biggest challenge in finding out why SMEs have a relatively low adoption of ERM approaches.

One limitation of this study could be the study sample, which focuses only on the Czech Republic. However, this study could be interesting for other Central European countries that have experienced similar historical events in the second half of the twentieth century. Another limitation of this research could be the subjective evaluation of the variables. However, to minimize the effects of this limitation, the authors conducted pilot tests and used validated constructs. Objective assessments of the variables within SMEs may not be feasible given the low level of disclosure related to ERM among SMEs.

Data availability

Data were collected by the private company Ipsos ( https://www.ipsos.com/cs-cz ) and is not publicly available.

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This study was funded by Prague University of Economics and Business, Faculty of Business Administration, grant number IGA VŠE F3/16/2021 “The relationship between the level of ERM and the economic performance of companies”.

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All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by JŠ and LS. The first draft of the manuscript was written by JŠ and LS and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Appendix 1: Description of the manifest variables

Authors: (Miloš Sprčić et al., 2017 ).

Retrieved from (Denison, 1990 ).

Retrieved from (Sax and Torp, 2015 ).

Retrieved from (Uhlaner et al. 2014 ).

Appendix 2: Initial model including all manifest variables

Appendix 3: Discriminant validity, reliability and inner VIF of the final model

• Source own calculation

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Syrová, L., Špička, J. Exploring the indirect links between enterprise risk management and the financial performance of SMEs. Risk Manag 25 , 1 (2023). https://doi.org/10.1057/s41283-022-00107-9

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Accepted : 10 September 2022

Published : 12 December 2022

DOI : https://doi.org/10.1057/s41283-022-00107-9

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