Using Numbers in Scientific Manuscripts

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When should you spell out a number in a scientific paper, and when do you use a numeral? Here's how to follow conventions and be consistent.

Updated on January 8, 2013

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Writing a scholarly manuscript often requires the use of numbers to express important information, particularly in the sciences. Although the use of numbers is largely straightforward, there are a few things to keep in mind. In this article, numeral refers specifically to a number as it is written in mathematics (e.g., 4).

Do not start a sentence with a numeral

When writing for publication, try to use spelled-out numbers at the beginning of a sentence in place of numerals. This distinction is not based on grammar, but rather the conventions of academic writing in English.

  • " 15 samples were collected " should be written as " Fifteen samples were collected "
  • At times, writing out the numeral at the beginning of the sentence would be particularly unwieldy. In such cases, it is preferable to rearrange the sentence such that the numeral is not placed at the beginning. For example, " 6579 patient charts were collected for analysis " could be altered to " Charts from 6579 patients were collected for analysis "
  • Note that some chemical compounds include numerals, and these should not be written out, even at the beginning of a sentence: " 5 -hydroxytryptamine is a neurotransmitter derived from tryptophan. "

Be consistent in the use of numerals or spelled-out numbers

Other tips for number usage involve consistency within your manuscript. As shown above, each number can be written as a numeral or a word. Many authors choose to use numerals for large numbers (say, those over 10) but words for small numbers. Either form is typically fine, but it is best to be consistent with your choice.

  • If " We collected a total of eight samples " is written in your Methods section, avoid writing " Samples from all 8 lakes were nearly identical in pH " in your Results. Either correct the first sentence to include a numeral ('8') or change the second to the spelled-out word 'eight.'
  • In addition, try to avoid mixing numerals and spelled-out words within a single sentence. For example, we suggest changing " The zoo has two pandas, eight elephants, and 15 orangutans " to " The zoo has two pandas, eight elephants, and fifteen orangutans ."

Other tips for consistency with numerals

Here are two other ways to make sure that your numerals are consistent within your manuscript. Consistency in your formatting choices is one way to demonstrate your attention to detail. Always consult your target journal's style sheet to see what they prefer.

  • When using numbers larger than 1000, be sure to format them all in the same way. For example, 156000 , 156,000 , and 156 000 are all acceptable, but use only one format in your document.
  • Be consistent with the inclusion or omission of a leading zero before decimals (i.e., 0.05 or .05 , but not both). Also, do not mix the use of a decimal point (0.12) with a decimal comma (0,12). In the vast majority of cases, journals prefer the use of the decimal point.

We hope that this article provides some guidance for the use of numbers in your writing. If you have specific questions about the numbers in your text, write to us by email at [email protected] . As always, AJE wishes you the best of luck with your research and publication!

Ben Mudrak, Senior Product Manager at American Chemical Society/ChemRxiv, PhD, Molecular Genetics and Microbiology, Duke University

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  • Reporting Statistics in APA Style | Guidelines & Examples

Reporting Statistics in APA Style | Guidelines & Examples

Published on April 1, 2021 by Pritha Bhandari . Revised on January 17, 2024.

The APA Publication Manual is commonly used for reporting research results in the social and natural sciences. This article walks you through APA Style standards for reporting statistics in academic writing.

Statistical analysis involves gathering and testing quantitative data to make inferences about the world. A statistic is any number that describes a sample : it can be a proportion, a range , or a measurement, among other things.

When reporting statistics, use these formatting rules and suggestions from APA where relevant.

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Table of contents

Numbers and measurements, decimal places and leading zeros, formatting mathematical formulas, formatting statistical terms, reporting means and standard deviations, reporting chi-square tests, reporting z tests and t tests, reporting analysis of variance (anovas), reporting correlations, reporting regressions, reporting confidence intervals, other interesting articles, frequently asked questions about apa style statistics.

In general, APA advises using words for numbers under 10 and numerals for 10 and greater . However, always spell out a number that appears at the start of a sentence (or rephrase).

You should always use numerals for:

  • Exact numbers before units of measurement or time
  • Mathematical equations
  • Percentages and percentiles
  • Ratios, decimals, and uncommon fractions
  • Scores and points on scales (e.g., 7-point scale)
  • Exact amounts of money

Units of measurement and time

Report exact measurements using numerals, and use symbols or abbreviations for common units of measurement when they accompany exact measurements. Include a space between the number and the abbreviation.

When stating approximate figures, use words to express numbers under 10, and spell out the names of units of measurement.

  • The ball weighed 7 kg.
  • The ball weighed approximately seven kilograms.

Measurements should be reported in metric units. If you recorded measurements in non-metric units, include metric equivalents in your report as well as the original units.

Percentages

Use numerals for percentages along with the percent symbol (%). Don’t insert a space between the number and the symbol.

Words for “percent” or “percentage” should only be used in text when numbers aren’t used, or when a percentage appears at the start of a sentence.

  • Of these respondents, 15% agreed with the statement.
  • Fifteen percent of respondents agreed with the statement.
  • The percentage was higher in 2020.

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The number of decimal places to report depends on what you’re reporting. Generally, you should aim to round numbers while retaining precision. It’s best to present fewer decimal digits to aid easy understanding.

The following guidelines are usually applicable.

Use two or three decimal places and report exact values for all p values greater than .001. For p values smaller than .001, report them as p < .001.

Leading zeros

A leading zero is zero before the decimal point for numbers less than one. In APA Style, it’s only used in some cases.

Use a leading zero only when the statistic you’re describing can be greater than one. If it can never exceed one, omit the leading zero.

  • Consumers reported high satisfaction with the services ( M = 4.1, SD = 0.8).
  • The correlation was medium-sized ( r = .35).
  • Although significant results were obtained, the effect was relatively small ( p = .015, d = 0.11).

Provide formulas only when you use new or uncommon equations. For short equations, present them within one line in the main text whenever possible.

Make the order of operations as clear as possible by using parentheses (round brackets) for the first step, brackets [square brackets] for the second step, and braces {curly brackets} for the third step, where necessary.

More complex equations, or equations that take more than one line, should be displayed on their own lines. Equations should be displayed and numbered if you will reference them later on, regardless of their complexity. Number equations by placing the numbers in parentheses near the right edge of the page.

\begin{equation*}\sqrt[3]{x}-3ac\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(1)\end{equation*}

When reporting statistical results , present information in easily understandable ways. You can use a mix of text, tables, and figures to present data effectively when you have a lot of numbers to report.

In your main text, use helpful words like “respectively” or “in order”  to aid understanding when listing several statistics in a sequence.

The APA manual provides guidelines for dealing with statistical terms, symbols and abbreviations.

Symbols and abbreviations

Population parameters are often represented with Greek letters, while sample statistics are often represented with italicized Latin letters.

Use the population symbol ( N ) for the total number of elements in a sample, and use the sample symbol ( n ) for the number of elements in each subgroup of the full sample.

In general, abbreviations should be defined on first use, but this isn’t always the case for common statistical abbreviations.

Capitalization, italicization and hyphenation

Statistical terms such as t test, z test, and p value always begin with a lowercase, italicized letter. Never begin a sentence with lowercase statistical abbreviations.

These statistical terms should only be hyphenated when they modify a subsequent word (e.g., “ z -test results” versus results of “ z tests”).

You can form plurals of statistical symbols (e.g., M or p ) by adding a non-italicized “s” to the end with no apostrophe (e.g., M s or p s).

In general, the following guidelines apply.

Parentheses vs. brackets

Always aim to avoid nested parentheses and brackets when reporting statistics. Instead, you should use commas to separate related statistics.

  • Scores improved between the pretest and posttest ( p < .001).
  • Significant differences in test scores were recorded, F (1, 30) = 4.67, p = .003.
  • (A previous meta-analysis highlighted low effect sizes [ d = 0.1] in the field).

Report descriptive statistics to summarize your data. Quantitative data is often reported using means and standard deviations, while categorical data (e.g., demographic variables) is reported using proportions.

Means and standard deviations can be presented in the main text and/or in parentheses. You don’t need to repeat the units of measurement (e.g., centimeters) for statistics relating to the same data.

  • Average sample height was 136.4 cm ( SD = 15.1).
  • The height of the initial sample was relatively low ( M = 125.9 cm, SD = 16.6).
  • Height significantly varied between children aged 5–7, 8–10, and 11–13. The means were 115.3, 133.5, and 149.1 cm, respectively.

To report the results of a chi-square test , include the following:

  • the degrees of freedom ( df ) in parentheses
  • the chi-square (Χ 2 ) value (also referred to as the chi-square test statistic)
  • the p value
  • A chi-square test of independence revealed a significant association between gender and product preference, Χ 2 (8) = 19.7, p = .012.
  • Based on a chi-square test of goodness of fit , Χ 2 (4) = 11.34, p = .023, the sample’s distribution of religious affiliations matched that of the population’s.

For z tests

To report the results of a z test, include the following:

  • the z value (also referred to as the z statistic or z score)
  • The participants’ scores were higher than the population average, z = 2.48, p = .013.
  • Higher scores were obtained on the new 20-item scale compared to the previous 40-item scale, z = 2.67, p = .007.

For t tests

To report the results of a t test , include the following:

  • the t value (also referred to as the t statistic)
  • Older adults experienced significantly more loneliness than younger adults, t (32) = 2.94, p = .006.
  • Reaction times were significantly faster for mice in the experimental condition, t (53) = 5.94, p < .001.

To report the results of an ANOVA , include the following:

  • the degrees of freedom (between groups, within groups) in parentheses
  • the F value (also referred to as the F statistic)
  • A one-way ANOVA demonstrated that the effect of leadership style was significant for employee engagement, F (2, 78) = 4.58, p = .013.
  • We found a statistically significant main effect of age group on social media use, F (3, 117) = 3.19, p = .026.

To report the results of a correlation, include the following:

  • the degrees of freedom in parentheses
  • the r value (the correlation coefficient)
  • We found a strong correlation between average temperature and new daily cases of COVID-19, r (357) = .42, p < .001.

Results of regression analyses are often displayed in a table because the output includes many numbers.

To report the results of a regression analysis in the text, include the following:

  • the R 2 value (the coefficient of determination)

The format is usually:

  • SAT scores predicted college GPA, R 2 = .34, F (1, 416) = 6.71, p = .009.

You should report confidence intervals of effect sizes (e.g., Cohen’s d ) or point estimates where relevant.

To report a confidence interval, state the confidence level and use brackets to enclose the lower and upper limits of the confidence interval, separated by a comma.

  • Older adults experienced significantly more loneliness than younger adults, t (32) = 2.94, p = .006, d = 0.81, 95% CI [0.6, 1.02].
  • On average, the treatment resulted in a 30% reduction in migraine frequency, 99% CI [26.5, 33.5].

When presenting multiple confidence intervals with the same confidence levels in a sequence, don’t repeat the confidence level or the word “CI.”

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

  • Chi square test of independence
  • Statistical power
  • Descriptive statistics
  • Degrees of freedom
  • Pearson correlation
  • Null hypothesis

Methodology

  • Double-blind study
  • Case-control study
  • Research ethics
  • Data collection
  • Hypothesis testing
  • Structured interviews

Research bias

  • Hawthorne effect
  • Unconscious bias
  • Recall bias
  • Halo effect
  • Self-serving bias
  • Information bias

According to the APA guidelines, you should report enough detail on inferential statistics so that your readers understand your analyses.

Report the following for each hypothesis test:

  • the test statistic value
  • the degrees of freedom
  • the exact p value (unless it is less than 0.001)
  • the magnitude and direction of the effect

You should also present confidence intervals and estimates of effect sizes where relevant.

Use one decimal place for:

  • Standard deviations
  • Descriptive statistics based on discrete data

Use two decimal places for:

  • Correlation coefficients
  • Proportions
  • Inferential test statistics such as t values, F values, and chi-squares.

In APA style, statistics can be presented in the main text or as tables or figures . To decide how to present numbers, you can follow APA guidelines:

  • To present three or fewer numbers, try a sentence,
  • To present between 4 and 20 numbers, try a table,
  • To present more than 20 numbers, try a figure.

Since these are general guidelines, use your own judgment and feedback from others for effective presentation of numbers.

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Other APA Guidelines: Numbers

Basics of numbers.

Per APA 7, Section 6.32, use numerals to express numbers 10 or above (e.g., 11, 23, 256). Per Section 6.33, write out numbers as words to express numbers up to nine (e.g., three, seven, eight).

Take the APA Style Diagnostic Quiz  to test your knowledge.

Numbers Expressed as Words

Use words to express numbers in these situations:

Seventeen computer programmers went out to dinner last night
The principal presented awards to three fourths of the student body.
(This is a new rule in APA 7. APA 6 recommended using numerals in the abstract.)

Numbers Expressed as Numerals

Use numerals to express numbers in these situations:

She had been a nurse for 3 years.
Chapter 4 was considered required reading.
The student scored a perfect 7.
Each post was roughly 2.45 ft apart.
Teachers gave students ice cream if they scored in the top 5%.
You owe me $5.

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Numbers in APA

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Note:  This page reflects the 6th edition of the APA manual, which is now out of date. It will remain online until 2021, but will not be updated. There is currently no equivalent 7th edition page, but we're working on one. Thank you for your patience. Here is a link to our APA 7 "General Format" page .

In general, APA style recommends using words to express numbers below 10, and using numerals when expressing numbers 10 and above. See below for a more extensive list.

Numbers expressed as numerals

In addition to expressing numbers 10 and above, the following are other instances when you would use numerals rather than words:

Numbers mentioned in the abstract, a table, or a figure in the paper (this allows for brevity) 

This study consisted of 8 tests.

Numbers that immediately precede a unit of measurement

2.54 cm, 1.5 gal

Numbers that represent statistical or mathematical functions, fractional or decimal quantities, percentages, ratios, percentiles, and quartiles

Divided by 10

50% of the participants

a ratio of 10:1

the 10 th percentile

numbers that represent time, dates, ages, scores and point values on a scale, exact sums of money, and numerals

2 hr 30 min

50-year-olds

A 10-point scale

Exception: Use words for approximations of numbers of days, weeks, months, or years

Roughly six months ago

Numbers that denote a specific place in a numbered series, parts of books and tables, and each number in a list of four or more numbers

Illustration 1

Numbers expressed as words

In addition to using words to express numbers below 10, use words to also express:

Numbers beginning a sentence, title, or text heading

Fifteen participants were in the control group.

Common fractions

Three fourths of the population

Common phrases or groups

Seven Wonders of the World

The Three Musketeers

Other Rules Concerning Numbers

Here are a few more rules concerning numbers to adhere to as you follow APA style:

If you are using two modifiers against a noun, use a combination of both numerals and words

Three 5-point scales

If you’re unsure which modifier to write and which to express numerically, try it both ways. Be sure the way you express the numbers is in the clearest way possible.

Place a zero before a decimal fraction less than 1 if the statistic can exceed 1.

If the statistic cannot exceed 1, you do not need a zero.

For more specific guidelines, talk to your instructor or refer to the Style Manual.

Writing academically: Numbers

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When using numbers in academic writing you need to decide if it’s more appropriate to use a numeral (e.g. 9) or to write the number in words (e.g. nine). It’s worth checking to see if your department has specific advice on this matter, because individual approaches do vary. In the absence of specific advice, here is some general guidance on the matter:

Basic numbers

  • Numbers  up to nine  should always be written in  words,  anything higher than nine can be written in numerals. Alternatively, some guides suggest that if you can write the number in two words or fewer then use words rather than numerals. If you are going to take this approach then you should include a hyphen when writing numbers with two words, e.g. twenty-seven.
  • For larger numbers, it is acceptable to use either numerals or words depending on context (e.g. a thousand people/1,000 people), but you should always use numerals in technical writing, e.g. 200,000 km. For less precise larger numbers, the written form is better (e.g. several thousand).

Measurements and decimals/fractions

  • Use numerals for units of measurement or time, e.g. 500 km, 10 minutes.
  • Always use numerals for decimals and fractions (e.g. 0.5 cm) unless the figures are vague (e.g. around half of the population).
  • Units of measurement that modify a noun should be hyphenated, e.g. a 3-year-old child.

Dates, money and time

  • Always use numerals for dates, e.g Monday 4 April, 2016.
  • Use numerals for money (e.g. His pocket money was exactly £1.00 per week) unless the amounts are vague (e.g. He earned well over a million last year).
  • Use numerals for indicating the precise time (e.g. 08:00), or words if the times indicated are vague (e.g. around eight o’clock). 

Combining numbers

  • If you need to combine two numbers that run together then use words for the shorter number and numerals for the longer number, e.g. a tower of 1000 ten-pence pieces. 

Starting sentences with numbers

  • Avoid starting a sentence with a numeral. Either write the number in words or rearrange your sentence. For example, “Three hundred and sixty-five days make one year” could become “There are 365 days in a year”. If you start a sentence with a year, write “The year” first e.g. “The year 1066 saw one of the most famous battles in English history”.
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Numbers In Academic Writing – APA Style Guidelines

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Numbers-in-academic-writing-Definition

Numbers are an imperative part of academic writing , serving as vital tools to represent quantitative data, statistical data, or measures in an accurate and precise manner. Numbers are used across various fields, including sciences, humanities, and business. However, adherence to specific rules is necessary in terms of using numbers effectively in academia, which vary depending on the style guide followed. This article will provide insights into how numbers are used appropriately.

Inhaltsverzeichnis

  • 1 Numbers in Academic Writing – In a Nutshell
  • 2 Definition: Numbers in academic writing
  • 3 Numbers in academic writing: Exceptions
  • 4 Numbers in academic writing: Percentages
  • 5 Numbers in academic writing: Statistical results
  • 6 Numbers in academic writing: Measurements
  • 7 Numbers in academic writing: Long numbers

Numbers in Academic Writing – In a Nutshell

  • Academic writing uses numbers in distinct ways depending on style guide.
  • Conventions apply to technical number writing and non-technical number writing.
  • Numbers are usually written out from one to nine, and numerals are used from 10.
  • Technical data and statistics should always appear as numerals for reference.

Definition: Numbers in academic writing

The APA Style is one of the most widely used academic writing styles and is largely adopted by the behavioral and social sciences. A number can be written both numerically or in words within this style.

Typically, a number from one to nine should be written out as words, while numbers from 10 and above should be written out numerically. This general rule also applies to ordinals (first, 10th). Some exceptions do apply, as found next in this article.

Other writing styles utilize different number rules. The Chicago style , for instance, requires numbers to be written out as words up to 100. The MLA style spells out all numbers that can be written within one or two words (three, one hundred, etc.).

Numbers in academic writing: Exceptions

Exceptions to the general rule above apply in the following cases:

1. All numbers should be represented numerically when they are detailing an exact unit of measurement.

  • The rock was chiseled 6 cm deep.

2. Write out numerals as words when they begin a sentence, except when dealing with specific years.

  • Eighteenth-century scientists advanced the practice of medicine
  • 1921 marked the discovery of insulin.

3. A number should be written out when dealing with fractions, set expressions, or other known numeric titles.

  • John Milton crafted the poem in 1626, also referred to as the Fifth of November poem.
  • According to sources, one-third of the English population perished from the Black Death.
  • Orwell’s Nineteen Eighty-Four is set in an alternative world in the year 1984 .

Numbers in academic writing: Percentages

When dealing with percentages in the APA Style, use numerals followed by the percent sign % , instead of “percent” or the abbreviations, “pct.”, “pct,”, or “pc”.

  • The Spanish flu affected over 25% of the US population.

The same rule when beginning sentences with numerals applies to percentages, i.e., they should be written out as words when they start a sentence.

  • Twenty-five percent of the US population was affected.

Numbers in academic writing: Statistical results

Reporting statistics in APA and papers that deal with technical numerical language in qualitative research have their own rules.

Here, all data is written in numerals to remain consistent and easily digested. This applies to the main body, tables, and figures sections of a paper.

Other statistical conventions include:

  • Report the majority of statistics to two decimal places.
  • Report statistics that can’t exceed 1.0 to three decimal places.
  • For values that could exceed 1.0, use a leading zero. Those that can’t exceed 1.0 do not feature a leading zero.
  • Italicize statistical values that aren’t Greek letters. E.g. SD .
  • Spaces should be left before and after equal, more-than, and less-than signs.

Numbers in academic writing: Measurements

Always use numerals for units of measurement.

  • Ampules contain 100 mg in 2 ml .

Numerals should be used for precise ages, timescales, dates, score lines, points of scale, and monetary sums.

  • The final score was France 4 , and Croatia 2 .
  • The students were aged 18 to 21 years in the study.

Imprecise ages and generalizations are not numbered but written out.

  • She was roughly six years old based on his estimation.
  • The outcome will be approximately seven times .

Numbers in academic writing: Long numbers

Longer numbers have their own set of rules. A period should be used to indicate a decimal point.

Commas are to be used to separate large figures every three digits after 1,000.

For sums exceeding 6 numerals, like 1 million and 1 billion, use a combination of numerals and written language.

  • HBO Max had 73.8 million subscribers in 2022.
  • This is a considerable growth from its 800,000 subscribers in 2015.

Should you write out numbers in academic writing?

As a general rule of thumb, numbers up to nine should be written out in the APA Style, while anything exceeding 10 should appear as numerals.

How are dates written in academic writing?

Dates are always written as numerals.

How are numbers expressed at the beginning of a sentence?

They are written out when they begin a sentence, except for dates and technical data.

Should I use the word "percent" or its symbol "%"?

The APA Style states that the symbol “%” should be used after numerals, while “percent” should be used for written-out figures.

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Numbers in Scientific Manuscripts: What Are the Rules?

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Enago Academy

Numbers in Writing: Guidelines for Life Sciences and Medicine (Part 3)

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We hope that by now you are familiar with number conventions in formal writing. You can refer to Part 1 and Part 2 in this series, for a quick recap.

In this post, we will provide a simple rule of thumb and some exceptions for our biomedical authors.

While the style of literary texts is to spell out most numbers, that of scientific text is to use numerals when a degree of accuracy is intended. The modern scientific number style treats numbers more consistently by extending the use of “numerals” to most 1-digit whole numbers (1 to 9) that were previously expressed as words (one to nine). This style allows all quantities to be expressed in a similar manner. In addition, numerals have greater visual distinctiveness than words; it increases the profile of quantities in running text.

This article covers guidelines on scientific number style as recommended by the two predominant style guides in life sciences and medicine:

  • Scientific Style and Format: The CSE Manual for Authors, Editors, and Publishers ( CSE )
  • American Medical Association Manual of Style: A Guide for Authors and Editors ( AMA )

In actual application of these guidelines, however, when common sense or editorial judgment says a guideline is a poor choice for a specific document, follow sense or judgment.

Rule of Thumb

In a scientific text, Arabic numerals should be used in preference to words when the number designates anything that can be counted or measured.

For example,

  • The authors detected VEGF in 12 of 12 samples from patients with NVG.
  • We started the experiment with just 5 books (see Figure 1).

The rest of this article discusses six exceptions to this rule.

Exception 1: Beginning a Sentence, Title, Heading

Numerals are not used to begin a sentence, title, or heading. If logic calls for a number to begin a sentence, title, or heading, then spell out the number. If possible, reword so that the number appears elsewhere or connect the sentence to the previous or next sentence.

  • Avoid: 35 cm is the preferred minimum operational snow base. However, ski areas in the study region produced a thicker snow base (usually 50−75 cm) early in the ski season.
  • Spell out: Thirty-five centimeters is the preferred minimum operational snow base. However, ski areas in the study region produced a thicker snow base (usually 50−75 cm) early in the ski season.
  • Reword: Although 35 cm is the preferred minimum operational snow base, ski areas in the study region produced a thicker snow base (usually 50−75 cm) early in the ski season.
Related: Need instant academic writing tips on your cell phone? Download the FREE Enago Academy mobile app now!

Spelling Tip!

When spelling out numerals, hyphenate numbers from twenty-one through ninety-nine when these numbers occur alone or as part of a larger number. When numbers greater than 100 are spelled out, do not use commas or “and” (e.g., one hundred forty-four).

Exception 2: Adjacent Numbers

When two numbers are adjacent, spell out the number most easily expressed in words and leave the other as a numeral, or reword the sentence to separate the numbers. In general, retain the numeral that occurs with a unit of measurement.

  • Avoid: The fat content of the lesions could be identified on 3 10-mm sections.
  • Spell out: The fat content of the lesions could be identified on three 10-mm sections.
  • Reword: The fat content of the lesions could be identified on three sections of 10 mm each.

Exception 3: Zero (0) and One (1)

For these numbers, applying consistent logic (numerals for quantities and words otherwise) may make decisions about correct usage more difficult as they are also used in ways that are more like figures of speech than precise quantifications (“in one of the subjects…,” “zero-point energies”).

Express the whole numbers zero and one as numerals only when:

  • they are connected to a unit of measure (1 year, 1 mm, 0 A, etc.)
  • they are used as assigned or calculated values (when z = 0, a mean of 1)
  • are part of a series or are closely linked with numbers other than 0 or 1 (0, 1, 5, and 9 were…, between 0 and 2)

Otherwise, spell out zero and one:

  • …compared to the standard one (one used as a pronoun)
  • one of the doctors (when “one” can be replaced with “a” or “a single”)
  • on the one hand (transition phrase)
  • zero-based budgeting (terms)
  • one of whom could have been the leader (when emphasis on the quantity (0 or 1) would be confusing)

Exception 4: Accepted Usage/Idiomatic Expressions

When a number is used idiomatically or within a figure of speech, spell out the word; however, like jargon, figures of speech may be inappropriate for scientifically oriented writing because they may not be readily understood by readers whose first language is not English. Recasting the phrase is generally the better option.

  • Avoid: We logged his sessions to learn a thing or 2, and warn his subsequent targets.
  • Spell out: We logged his sessions to learn a thing or two, and warn his subsequent targets.
  • Reword: We logged his sessions to learn some moves, and warn his subsequent targets.

Exception 5: Ordinal Numbers

In general, spell out single-digit ordinals (corresponding to the numbers 1 to 9), whether adjectives or adverbs.

  • for the ninth time but for a 10th time
  • were first discovered
  • the third test run but the 98th test run

When there is a mix of single-digit and larger ordinals and double-digit ordinals, the express single-digit ordinals in the numeric form:

  • Avoid: These correspond to daily values between the first and 15th of August 2003.
  • Numeric Form: These correspond to daily values between the 1st and 15th of August 2003.

Exception 6: Common Fractions

In general, common fractions should be spelled out in running text.

  • half of the books
  • nearly three-quarters of the sample
  • a two-thirds majority

When the precise value must be conveyed, the decimal or percent form is preferred.

Would you like to try out a quick quiz to test your number knowledge? Check out these easy and fun exercises from GrammarBook : Exercise 1 and Exercise 2

Comment below to let us know how you fared! All the best!

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Guidelines and Rules for Presenting Numbers in Research Papers

Updated: May 7, 2020

Since numbers are at the heart of research, you should know common rules regarding presenting numbers representing quantitative data in research papers. Knowing these rules will be helpful for writing the material and method section as well as other sections of the paper. If you are aiming to publish in a scientific or scholarly journal, you should check the Guidelines for Authors page of the journal you are targeting for the specific style guide that they follow. Since there are some variations found in different style guides, this will be important to know which guide they adopt. If they do not give this sort of information, it can be helpful to follow some common guidelines prescribed from respected sources like the Council of Scientific Editors. For more detailed coverage of presenting numbers, statistics and mathematical equations in research papers check out: Scientific Style and Format: The CSE Manual for Authors, Editors, and Publishers, The Chicago Manual of Style, and How to Report Statistics in Medicine. My apologies for instances where certain math characters were lost in copying below, specifically those related to exponents and superscript in scientific notation.

1. In scientific and technical texts, with a focus on quantitative data, represent a number with its numeral form, not word form:

312 base pairs

2. Use the numeral form when comparing with numbers:

A total of 5 out of 24 of the respondents dropped out of the study.

NOT: A total of five out of twenty four of the respondents dropped out of the study.

3. Do not begin a sentence with a digit; instead use the word form for the number in question, even if it is above eleven:

Fifty-six rats were used.

NOT: 56 rats were used.

Or rewrite the sentence instead of beginning with a lengthy word:

A total of 4,589 moths were collected.

NOT: Four thousand five hundred eighty-nine moths were collected.

4. Separate every three digits with a comma, except with numbers after a decimal. Use a period as a decimal point, and not a comma:

3,000 participants completed the survey.

NOT: 3.000 participants completed the survey.

5. Be careful with compound nouns that report numbers. All words preceding the head noun must be singular since they function like adjectives. In English, adjectives are always singular:

A 36-day-old rat.

NOT: a 36 days old rat.

6. The terms twice vs. two times have essentially the same meaning, except that twice might be favored for being shorter.

The specimens were disrupted by sonication two times for 45 s at 5°C.

The specimens were disrupted by sonication twice for 45 s at 5°C.

7. The term circa is used with historical dates, but not typically with measurements. Likewise, the symbol, “” means approximately. Only use it in math applications, not in prose. Instead, use the word “approximately” in running text:

The temple was destroyed circa 1432 BCE.

Approximately 542 birds were sighted.

NOT: Circa 542 birds were sighted.

Approximately 2ml was added to the buffer.

NOT: Circa 2ml was added to the buffer.

The temperature was approximately 35C

NOT: The temperature was “” 35

8. Avoid imprecise expressions such as a 3-fold rise, 2-fold increase, two times as much , but instead use a more precise numerical percentage or decimal point when reporting precise quantities. This form can be used in a context where an approximation is acceptable, yet the number form should be used, not the word form:

3-fold increase NOT: threefold increase

9. When describing a decade use this form:

In the 1970s

During the 1980s

NOT: In the 70’s

NOT: In the Seventies

NOT: I n the 70s

10. Ordinals are commonly used in English to focus on rank, order or a sequence of certain quantitative data. They can be represented in numerical form or word form; for example, 1st, 2nd, 3rd, 4th, first, second third, and fourth. Do not confuse their form:

Eleventh, twelfth, thirteenth,…

NOT: eleventeen, twelveteen,…

As the CSE points out, “Ordinal numbers generally convey rank order, not quantity. Rather than being expressly enumerative (answering the question “How many?”), ordinals often describe “which”, “what”, or “in what sequence”. Because this function of ordinals is more prose-oriented than quantitative, distinctiveness within the text is less important for ordinal numbers, and undisrupted reading flow and comprehension take precedence”. Hence use the word form for ordinal numbers under 10:

The second wave toppled the wall.

The third sample contained only sediment.

The ninth patient quit the study due to family issues.

Use the numeric form for larger numbers above 10 as the word forms can be lengthy and awkward:

The 15th attempt was successful.

The 25th test was incomplete.

We focused on the 19th century.

The 97th test run

NOT: The ninety-seventh test run

The 21st Century

NOT: twenty-first Century

The numeric form can be used for numbers under 10 if they referred to repeatedly:

We surveyed 8 subjects: the 1st was most coherent, the 3rd, 4th, and 6th were contradictory, while the 5th, 7th, and 8th were moderately coherent; yet t he 1st could not recall the incident, and the 6th and 8th provided highly specific details of certain events.

Do not use an ordinal when writing the complete date:

February 7, 2014.

NOT: February 7th, 2014.

Use the short numerical form rather than the longer word form when discussing centuries:

Then 19thCentury

NOT: The nineteenth Century

11. Use the percent symbol (%) whenever a numeral accompanies it. Also, use no space between the number and the percent symbol:

NOT: 0.053 percent

NOT: 0.053 %

12. When two numbers are adjacent, for the sake of readability, spell out one and leave the other as a numerical form:

As shown in Table 2, three were not recovered.

NOT: As shown in Table 2, 3 were not recovered.

13. In running text in general, fractions should be represented in word form, rather than numerals. All two-word fractions should be hyphenated, whether as a noun or adjective form.

Roughly one-tenth of the study subjects reported adverse effects.

Two-thirds of this species is found in Brazil.

Nearly three-quarters of the respondents were pleased with the outcome .

Yet, for fraction quantities greater than one, use mixed fractions when you do not intend to give a precise value:

The study site was approximately 3¾ kilometers from the river.

The study ran for about 2½ years.

When a more precise value is desired, use a percentage or decimal form of the number.For mixed numbers with built up fractions, place the whole number close to the fraction, but for solid fractions, place a space between the whole number and the fraction:

Built up fraction: 9

Solid fractions: 9 2/3

14. With numbers that are less than 1.0, use an initial zero to the left of the decimal point:

0.345 NOT: .345

NOT: P = .05

15. When reporting quantities, consider what unit of measurement and decimal place is most meaningful to report. Round numbers to the most relevant and meaningful digit. For example, while reporting the average length of a group of fish, reporting centimeters would be the most meaningful unit to report. For example, it would be meaningful to report an average length of fish as 12 cm, and it might even be meaningful to report the tenths of Cen termers as in 12.4 cm, yet it would not be necessary to report in hundreds 12.37 cm or thousands of centimeters as in 12.372 cm. Reporting too many decimal points can be distracting to the reader and have little scientific importance. For example, note how it is easy to grasp the general pattern of weight gain in the following two sentences:

We noticed an average weight gain of 14.4529 g for college students, 12.39815 g for retired couples and 2.99277 g for single parents.

We noticed an average weight gain of 14 g for college students, 12 g for retired couples and 3g for single parents.

16. When reporting percentages, if the sample you are considering is less than 100, then round to whole numbers. With samples larger than 100, it could be meaningful to report one decimal point. Yet, consider how it will improve the readability and importance of the number. Note this pattern in the sentences below:

Of the 23 students studied, 32% (7 students) reacted favorably, 49% (11 students) had a neutral response, and 19% (4 students) had an adverse reaction to the practice.

NOT: Of the 23 students studied, 32.432% (7 students) reacted favorably, 48.983% (11 students) had a neutral response, and 18.594% (4 students) had an adverse reaction to the practice.

17. In research papers, numbers typically combine with units of measure or symbols, as specified and defined by the International System of Units (Système International d’Unités). These symbols can be alphabetical ( e.g., kg, μg, K, mol, A, s, Hz, mm, mL, min, g, cm) or non-alphabetical (e.g., $, %, S, £, °, ¹). As a general rule, numerals should always accompany these symbols:

A 25.0 mL  aliquot of 0.25 M HCNO (weak acid) is titrated with 0.15 M NaOH.

Near lead smelters and battery plants, air levels typically ranged from 0.3 to 4.0 μg/m3

18. Separate symbols from numbers with a single space:

19. Close up the space between a non alphabetical symbol and a number:

Note, one exception to this rule: The Council of Scientific Editors recommend a space here, while the American Medical Association recommends no space:

CSE Style: 45 °C

AMA Style: 45°C

Ultimately, you will need to follow the style guide recommendations from the journal that you planning to submit your research paper to.

21. When representing numbers in a range, use the word “to” between numbers, and not a hyphen or a dash:

Regional unemployment rates ranged from 1.2% to 33.3%.

NOT: Regional unemployment rates ranged from 1.2% - 33.3%.

When using the preposition “between” to introduce a range, always accompany it with “and”, not a hyphen or a dash:

In a range between 4 and 10cm.

NOT: In a range between 4 - 10cm.

When the range includes numbers with several digits, do not leave out the leading numbers of the second number of the range:

1958 to 1962

NOT: 1958 to 62

1,724 to 1,736

NOT: 1,724 to 36

You can use a single unit symbol alone after second number in a range of numbers, except for when the symbol is non-alphabetical and must be closed up to the number (e.g., $,%).

30 to 45 mL

120 to 200 Hz

10 to 20 min

NOT: 40 to $60

NOT: 13 to 22%

Be careful when expressing a change in value in a range, especially when using terms like “increased”, “decreased” or “changed”. Use language that clarifies that the change is in the range or in the final amount.

Growth increased by a range of 1.5 g/d to 3.5 g/d.

Growth increased from an initial value a range of 1.5 g/d to a final value of 3.5 g/d.

NOT: Growth increased by 1.5 g/d to 3.5 g/d.

NOT: Growth increased from 1.5 g/d to 3.5 g/d.

22. When reporting dimensions, use a multiplication symbol and not the letter “x” or the word “by”, and leave a space between the multiplication symbol and the numbers:

NOT: 22 by 18 by 16

When the focus is on expressing one range changing to a new range, place a hyphen between numbers to improve readability:

increased from 25–34 mm to 28–42 mm 

NOT:  increased from 25 to 34 mm to 28 to 42 mm

23. For a series of numbers, place the symbol after the last number, except in cases where the symbol must be close to a number:

14, 15, 18, and 54 Hz

$21, $37, and $41

10%, 14% and 34%

24. Express large numbers or very small number in powers of 10, scientific notation.

NOT: 38,000

NOT: 735,000,000

NOT: 0.000,003,51

25. For large numbers that are not expressing high precision, a combination of numbers and words are acceptable:

The population is around 25 million.

NOT: The population is around 25, 000, 000.

26. With common symbols of math operations ( separate the symbol and number with a space or thin space. Use the math symbol and not the letter x to represent multiplication. Do not use these sybmols in running text:

The averages equaled the total of all samples from plot A plus plot B.

NOT: The averages = the total of all samples from plot A + plot B.

When these symbols are used as modifiers of words, then close up the space between them and the term they modify. Also, do not place two or more operator symbols side by side.

Also, do not place two or more operator symbols side by side.

The total was greater than

NOT: The total was

27. For symbols used in calculus, refer to the Association of American Publishers for extensive details directions on their markup in manuscripts. For details on how to present vectors, scalars, tensors, matrices and determinants, see Scientific Style & Format: The Council of Scientific Editors, Chapter 12.

28. Brackets, parentheses, and braces in mathematics are referred to as enclosures or “fences”. In math, their order of use is parentheses within brackets within braces, and the reverse is order follows in non-mathematical prose: braces within brackets within parentheses.

mathematics: { [ ( ) ] }

prose or non-mathematics: ( [ {} ] )

29. In the following math expressions no space (closed up to the number) is required:

When expressing multiplication without the multiplication symbol:

Between fences and enclosures and the variables on either side of them:

(2p − 6bc)(1 − a)

 Between terms and their subscripts as in the following terms:

With the symbols plus and minus when used to indicate positive or negative value for numbers:

When expressing a ratio using a colon, close up the space:

Place a space between all common math operators: +, =, -,

30. Ratios, percentages, and proportions are commonly used to simplify and report research findings. Whenever using them, be sure to report a numerator and denominator of that accompanies them; otherwise it will be difficult to interpret them in a meaningful way. For instance 50% could be 2 of 4 samples had a positive result or 6,000 of 12,000 had a positive result. While both are examples of 50%, they would have a very different meaning in research. Separate the two numbers of a ratio by a colon, with the first typically being the numerator and the second the denominator:

The ratio of negative results was 3 to1 (946:329).

NOT: The ratio of negative results was 3 to1.

Proportions are the result of dividing the numerator by the denominator, with the numerator typically a subset of the items in the denominator:

The proportion of subjects experiencing adverse effects was 0.032 (21/651).

NOT: The proportion of subjects experiencing adverse effects was 0.032 .

To express a proportion as a percentage, multiply it by 100.

The percentage of subjects experiencing adverse effects 3.2% (21/651).

NOT: The percentage of subjects experiencing adverse effects 3.2% (21/651).

After studying the points made above about presenting numbers, correct the sentences below with errors related to numbers.

1. 4 assays were performed.

2. Measurements were made for just about one hundred and fifty snakes.

3. Since 80ies’ it has been shown that X plays a role in Y.

4. The 2th and 3th samples were negative.

5. This accounted for most of the total biomass.

6. Many informations can be found in the literature.

7. A lot of water was needed.

8. The deprotonated ion increased by about 2-fold.

9. For this case, the factor was just about 0.90, i.e. very close to one.

10. Three of percent of the samples were positive.

11. Each stock was valued at ten thousands of dollars.

12. Circa 10 mM was used.

13. 17x4=68

15. The total was

16. The population is around 25, 000, 000.

17. We found 15 % similarity.

18. The range increased from 25 to 34 mm to 28 to 42 mm.

19. As shown in table 3, 2 there was a significant increase.

20. The average cost per sample was 40 to $60

21. As many as 13 to 22% of the participants expreienced no adverse effect.

22. One tenth of the subjects reported improved vision.

23. We detected a difference of 0.000,003,51.

24. Statistical significance was set at .05

25. Rates ranged from 1.2% to 33.3%.

Check Answers Below:

Four assays were performed. Begin a sentence with the word form (four), not a digit (4). Measurements were taken for approximately 150 snakes. Since the 1980sit has been shown that X causes Y. The 2nd and 3rd were negative for… …Accounted for the majority of the biomass.a great deal of informationcan be found in the literature.A great deal of water was needed. Give a precise numerical percentage rather than something vague like “about 2-fold”.Avoid vague and informal term such as “just about” and “very close to”. Instead substitute “approximately” and “nearly”. Three percent of the samples were positive. Each stock was valued at ten-thousand dollars Approximately10 mM was used. (Use space between common math operators) 94 (use no space between numeral and exponent)The total was greater than (Avoid presenting two math operator symbols side by side).The population is around 25 million. (Use the word form when giving large imprecise numbers).We found 15% similarity. (No space between numerals and non-alphabetical symbols).The range increased from 25–34 mm to 28–42 mm. (When reporting a change of ranges, use a hyphen between numbers to improve readability).As shown in Table 3, three subjects dropped out. (When two numbers are adjacent, for the sake of readability, spell out one and leave the other as a numerical form).

20. The average cost per sample was $40 to $60 (When presenting a range, both numbers must be accompanied by the non-alphabetical symbol).

21. As many as 13% to 22% of the participants experienced no adverse effect. (When presenting a range, both numbers must be accompanied by the non-alphabetical symbol).

22. One-tenth of the subjects reported improved vision (hyphenate two-word fractions).

23. We detected a difference of 3.51 ´ 10-6 (write out very large or very small numbers in scientific notation)

24. Statistical significance was set at 0.05 (Place a zero before a decimal place.

25. Rates ranged from 1.2% to 33.3%. (Use the preposition “to” between numbers in a range, not a hyphen).

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How to Write a Research Paper

Use the links below to jump directly to any section of this guide:

Research Paper Fundamentals

How to choose a topic or question, how to create a working hypothesis or thesis, common research paper methodologies, how to gather and organize evidence , how to write an outline for your research paper, how to write a rough draft, how to revise your draft, how to produce a final draft, resources for teachers .

It is not fair to say that no one writes anymore. Just about everyone writes text messages, brief emails, or social media posts every single day. Yet, most people don't have a lot of practice with the formal, organized writing required for a good academic research paper. This guide contains links to a variety of resources that can help demystify the process. Some of these resources are intended for teachers; they contain exercises, activities, and teaching strategies. Other resources are intended for direct use by students who are struggling to write papers, or are looking for tips to make the process go more smoothly.

The resources in this section are designed to help students understand the different types of research papers, the general research process, and how to manage their time. Below, you'll find links from university writing centers, the trusted Purdue Online Writing Lab, and more.

What is an Academic Research Paper?

"Genre and the Research Paper" (Purdue OWL)

There are different types of research papers. Different types of scholarly questions will lend themselves to one format or another. This is a brief introduction to the two main genres of research paper: analytic and argumentative. 

"7 Most Popular Types of Research Papers" (Personal-writer.com)

This resource discusses formats that high school students commonly encounter, such as the compare and contrast essay and the definitional essay. Please note that the inclusion of this link is not an endorsement of this company's paid service.

How to Prepare and Plan Out Writing a Research Paper

Teachers can give their students a step-by-step guide like these to help them understand the different steps of the research paper process. These guides can be combined with the time management tools in the next subsection to help students come up with customized calendars for completing their papers.

"Ten Steps for Writing Research Papers" (American University)  

This resource from American University is a comprehensive guide to the research paper writing process, and includes examples of proper research questions and thesis topics.

"Steps in Writing a Research Paper" (SUNY Empire State College)

This guide breaks the research paper process into 11 steps. Each "step" links to a separate page, which describes the work entailed in completing it.

How to Manage Time Effectively

The links below will help students determine how much time is necessary to complete a paper. If your sources are not available online or at your local library, you'll need to leave extra time for the Interlibrary Loan process. Remember that, even if you do not need to consult secondary sources, you'll still need to leave yourself ample time to organize your thoughts.

"Research Paper Planner: Timeline" (Baylor University)

This interactive resource from Baylor University creates a suggested writing schedule based on how much time a student has to work on the assignment.

"Research Paper Planner" (UCLA)

UCLA's library offers this step-by-step guide to the research paper writing process, which also includes a suggested planning calendar.

There's a reason teachers spend a long time talking about choosing a good topic. Without a good topic and a well-formulated research question, it is almost impossible to write a clear and organized paper. The resources below will help you generate ideas and formulate precise questions.

"How to Select a Research Topic" (Univ. of Michigan-Flint)

This resource is designed for college students who are struggling to come up with an appropriate topic. A student who uses this resource and still feels unsure about his or her topic should consult the course instructor for further personalized assistance.

"25 Interesting Research Paper Topics to Get You Started" (Kibin)

This resource, which is probably most appropriate for high school students, provides a list of specific topics to help get students started. It is broken into subsections, such as "paper topics on local issues."

"Writing a Good Research Question" (Grand Canyon University)

This introduction to research questions includes some embedded videos, as well as links to scholarly articles on research questions. This resource would be most appropriate for teachers who are planning lessons on research paper fundamentals.

"How to Write a Research Question the Right Way" (Kibin)

This student-focused resource provides more detail on writing research questions. The language is accessible, and there are embedded videos and examples of good and bad questions.

It is important to have a rough hypothesis or thesis in mind at the beginning of the research process. People who have a sense of what they want to say will have an easier time sorting through scholarly sources and other information. The key, of course, is not to become too wedded to the draft hypothesis or thesis. Just about every working thesis gets changed during the research process.

CrashCourse Video: "Sociology Research Methods" (YouTube)

Although this video is tailored to sociology students, it is applicable to students in a variety of social science disciplines. This video does a good job demonstrating the connection between the brainstorming that goes into selecting a research question and the formulation of a working hypothesis.

"How to Write a Thesis Statement for an Analytical Essay" (YouTube)

Students writing analytical essays will not develop the same type of working hypothesis as students who are writing research papers in other disciplines. For these students, developing the working thesis may happen as a part of the rough draft (see the relevant section below). 

"Research Hypothesis" (Oakland Univ.)

This resource provides some examples of hypotheses in social science disciplines like Political Science and Criminal Justice. These sample hypotheses may also be useful for students in other soft social sciences and humanities disciplines like History.

When grading a research paper, instructors look for a consistent methodology. This section will help you understand different methodological approaches used in research papers. Students will get the most out of these resources if they use them to help prepare for conversations with teachers or discussions in class.

"Types of Research Designs" (USC)

A "research design," used for complex papers, is related to the paper's method. This resource contains introductions to a variety of popular research designs in the social sciences. Although it is not the most intuitive site to read, the information here is very valuable. 

"Major Research Methods" (YouTube)

Although this video is a bit on the dry side, it provides a comprehensive overview of the major research methodologies in a format that might be more accessible to students who have struggled with textbooks or other written resources.

"Humanities Research Strategies" (USC)

This is a portal where students can learn about four methodological approaches for humanities papers: Historical Methodologies, Textual Criticism, Conceptual Analysis, and the Synoptic method.

"Selected Major Social Science Research Methods: Overview" (National Academies Press)

This appendix from the book  Using Science as Evidence in Public Policy , printed by National Academies Press, introduces some methods used in social science papers.

"Organizing Your Social Sciences Research Paper: 6. The Methodology" (USC)

This resource from the University of Southern California's library contains tips for writing a methodology section in a research paper.

How to Determine the Best Methodology for You

Anyone who is new to writing research papers should be sure to select a method in consultation with their instructor. These resources can be used to help prepare for that discussion. They may also be used on their own by more advanced students.

"Choosing Appropriate Research Methodologies" (Palgrave Study Skills)

This friendly and approachable resource from Palgrave Macmillan can be used by students who are just starting to think about appropriate methodologies.

"How to Choose Your Research Methods" (NFER (UK))

This is another approachable resource students can use to help narrow down the most appropriate methods for their research projects.

The resources in this section introduce the process of gathering scholarly sources and collecting evidence. You'll find a range of material here, from introductory guides to advanced explications best suited to college students. Please consult the LitCharts  How to Do Academic Research guide for a more comprehensive list of resources devoted to finding scholarly literature.

Google Scholar

Students who have access to library websites with detailed research guides should start there, but people who do not have access to those resources can begin their search for secondary literature here.

"Gathering Appropriate Information" (Texas Gateway)

This resource from the Texas Gateway for online resources introduces students to the research process, and contains interactive exercises. The level of complexity is suitable for middle school, high school, and introductory college classrooms.

"An Overview of Quantitative and Qualitative Data Collection Methods" (NSF)

This PDF from the National Science Foundation goes into detail about best practices and pitfalls in data collection across multiple types of methodologies.

"Social Science Methods for Data Collection and Analysis" (Swiss FIT)

This resource is appropriate for advanced undergraduates or teachers looking to create lessons on research design and data collection. It covers techniques for gathering data via interviews, observations, and other methods.

"Collecting Data by In-depth Interviewing" (Leeds Univ.)

This resource contains enough information about conducting interviews to make it useful for teachers who want to create a lesson plan, but is also accessible enough for college juniors or seniors to make use of it on their own.

There is no "one size fits all" outlining technique. Some students might devote all their energy and attention to the outline in order to avoid the paper. Other students may benefit from being made to sit down and organize their thoughts into a lengthy sentence outline. The resources in this section include strategies and templates for multiple types of outlines. 

"Topic vs. Sentence Outlines" (UC Berkeley)

This resource introduces two basic approaches to outlining: the shorter topic-based approach, and the longer, more detailed sentence-based approach. This resource also contains videos on how to develop paper paragraphs from the sentence-based outline.

"Types of Outlines and Samples" (Purdue OWL)

The Purdue Online Writing Lab's guide is a slightly less detailed discussion of different types of outlines. It contains several sample outlines.

"Writing An Outline" (Austin C.C.)

This resource from a community college contains sample outlines from an American history class that students can use as models.

"How to Structure an Outline for a College Paper" (YouTube)

This brief (sub-2 minute) video from the ExpertVillage YouTube channel provides a model of outline writing for students who are struggling with the idea.

"Outlining" (Harvard)

This is a good resource to consult after completing a draft outline. It offers suggestions for making sure your outline avoids things like unnecessary repetition.

As with outlines, rough drafts can take on many different forms. These resources introduce teachers and students to the various approaches to writing a rough draft. This section also includes resources that will help you cite your sources appropriately according to the MLA, Chicago, and APA style manuals.

"Creating a Rough Draft for a Research Paper" (Univ. of Minnesota)

This resource is useful for teachers in particular, as it provides some suggested exercises to help students with writing a basic rough draft. 

Rough Draft Assignment (Duke of Definition)

This sample assignment, with a brief list of tips, was developed by a high school teacher who runs a very successful and well-reviewed page of educational resources.

"Creating the First Draft of Your Research Paper" (Concordia Univ.)

This resource will be helpful for perfectionists or procrastinators, as it opens by discussing the problem of avoiding writing. It also provides a short list of suggestions meant to get students writing.

Using Proper Citations

There is no such thing as a rough draft of a scholarly citation. These links to the three major citation guides will ensure that your citations follow the correct format. Please consult the LitCharts How to Cite Your Sources guide for more resources.

Chicago Manual of Style Citation Guide

Some call  The Chicago Manual of Style , which was first published in 1906, "the editors' Bible." The manual is now in its 17th edition, and is popular in the social sciences, historical journals, and some other fields in the humanities.

APA Citation Guide

According to the American Psychological Association, this guide was developed to aid reading comprehension, clarity of communication, and to reduce bias in language in the social and behavioral sciences. Its first full edition was published in 1952, and it is now in its sixth edition.

MLA Citation Guide

The Modern Language Association style is used most commonly within the liberal arts and humanities. The  MLA Style Manual and Guide to Scholarly Publishing  was first published in 1985 and (as of 2008) is in its third edition.

Any professional scholar will tell you that the best research papers are made in the revision stage. No matter how strong your research question or working thesis, it is not possible to write a truly outstanding paper without devoting energy to revision. These resources provide examples of revision exercises for the classroom, as well as tips for students working independently.

"The Art of Revision" (Univ. of Arizona)

This resource provides a wealth of information and suggestions for both students and teachers. There is a list of suggested exercises that teachers might use in class, along with a revision checklist that is useful for teachers and students alike.

"Script for Workshop on Revision" (Vanderbilt University)

Vanderbilt's guide for leading a 50-minute revision workshop can serve as a model for teachers who wish to guide students through the revision process during classtime. 

"Revising Your Paper" (Univ. of Washington)

This detailed handout was designed for students who are beginning the revision process. It discusses different approaches and methods for revision, and also includes a detailed list of things students should look for while they revise.

"Revising Drafts" (UNC Writing Center)

This resource is designed for students and suggests things to look for during the revision process. It provides steps for the process and has a FAQ for students who have questions about why it is important to revise.

Conferencing with Writing Tutors and Instructors

No writer is so good that he or she can't benefit from meeting with instructors or peer tutors. These resources from university writing, learning, and communication centers provide suggestions for how to get the most out of these one-on-one meetings.

"Getting Feedback" (UNC Writing Center)

This very helpful resource talks about how to ask for feedback during the entire writing process. It contains possible questions that students might ask when developing an outline, during the revision process, and after the final draft has been graded.

"Prepare for Your Tutoring Session" (Otis College of Art and Design)

This guide from a university's student learning center contains a lot of helpful tips for getting the most out of working with a writing tutor.

"The Importance of Asking Your Professor" (Univ. of Waterloo)

This article from the university's Writing and Communication Centre's blog contains some suggestions for how and when to get help from professors and Teaching Assistants.

Once you've revised your first draft, you're well on your way to handing in a polished paper. These resources—each of them produced by writing professionals at colleges and universities—outline the steps required in order to produce a final draft. You'll find proofreading tips and checklists in text and video form.

"Developing a Final Draft of a Research Paper" (Univ. of Minnesota)

While this resource contains suggestions for revision, it also features a couple of helpful checklists for the last stages of completing a final draft.

Basic Final Draft Tips and Checklist (Univ. of Maryland-University College)

This short and accessible resource, part of UMUC's very thorough online guide to writing and research, contains a very basic checklist for students who are getting ready to turn in their final drafts.

Final Draft Checklist (Everett C.C.)

This is another accessible final draft checklist, appropriate for both high school and college students. It suggests reading your essay aloud at least once.

"How to Proofread Your Final Draft" (YouTube)

This video (approximately 5 minutes), produced by Eastern Washington University, gives students tips on proofreading final drafts.

"Proofreading Tips" (Georgia Southern-Armstrong)

This guide will help students learn how to spot common errors in their papers. It suggests focusing on content and editing for grammar and mechanics.

This final set of resources is intended specifically for high school and college instructors. It provides links to unit plans and classroom exercises that can help improve students' research and writing skills. You'll find resources that give an overview of the process, along with activities that focus on how to begin and how to carry out research. 

"Research Paper Complete Resources Pack" (Teachers Pay Teachers)

This packet of assignments, rubrics, and other resources is designed for high school students. The resources in this packet are aligned to Common Core standards.

"Research Paper—Complete Unit" (Teachers Pay Teachers)

This packet of assignments, notes, PowerPoints, and other resources has a 4/4 rating with over 700 ratings. It is designed for high school teachers, but might also be useful to college instructors who work with freshmen.

"Teaching Students to Write Good Papers" (Yale)

This resource from Yale's Center for Teaching and Learning is designed for college instructors, and it includes links to appropriate activities and exercises.

"Research Paper Writing: An Overview" (CUNY Brooklyn)

CUNY Brooklyn offers this complete lesson plan for introducing students to research papers. It includes an accompanying set of PowerPoint slides.

"Lesson Plan: How to Begin Writing a Research Paper" (San Jose State Univ.)

This lesson plan is designed for students in the health sciences, so teachers will have to modify it for their own needs. It includes a breakdown of the brainstorming, topic selection, and research question process. 

"Quantitative Techniques for Social Science Research" (Univ. of Pittsburgh)

This is a set of PowerPoint slides that can be used to introduce students to a variety of quantitative methods used in the social sciences.

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Research Method

Home » Research Paper – Structure, Examples and Writing Guide

Research Paper – Structure, Examples and Writing Guide

Table of Contents

Research Paper

Research Paper

Definition:

Research Paper is a written document that presents the author’s original research, analysis, and interpretation of a specific topic or issue.

It is typically based on Empirical Evidence, and may involve qualitative or quantitative research methods, or a combination of both. The purpose of a research paper is to contribute new knowledge or insights to a particular field of study, and to demonstrate the author’s understanding of the existing literature and theories related to the topic.

Structure of Research Paper

The structure of a research paper typically follows a standard format, consisting of several sections that convey specific information about the research study. The following is a detailed explanation of the structure of a research paper:

The title page contains the title of the paper, the name(s) of the author(s), and the affiliation(s) of the author(s). It also includes the date of submission and possibly, the name of the journal or conference where the paper is to be published.

The abstract is a brief summary of the research paper, typically ranging from 100 to 250 words. It should include the research question, the methods used, the key findings, and the implications of the results. The abstract should be written in a concise and clear manner to allow readers to quickly grasp the essence of the research.

Introduction

The introduction section of a research paper provides background information about the research problem, the research question, and the research objectives. It also outlines the significance of the research, the research gap that it aims to fill, and the approach taken to address the research question. Finally, the introduction section ends with a clear statement of the research hypothesis or research question.

Literature Review

The literature review section of a research paper provides an overview of the existing literature on the topic of study. It includes a critical analysis and synthesis of the literature, highlighting the key concepts, themes, and debates. The literature review should also demonstrate the research gap and how the current study seeks to address it.

The methods section of a research paper describes the research design, the sample selection, the data collection and analysis procedures, and the statistical methods used to analyze the data. This section should provide sufficient detail for other researchers to replicate the study.

The results section presents the findings of the research, using tables, graphs, and figures to illustrate the data. The findings should be presented in a clear and concise manner, with reference to the research question and hypothesis.

The discussion section of a research paper interprets the findings and discusses their implications for the research question, the literature review, and the field of study. It should also address the limitations of the study and suggest future research directions.

The conclusion section summarizes the main findings of the study, restates the research question and hypothesis, and provides a final reflection on the significance of the research.

The references section provides a list of all the sources cited in the paper, following a specific citation style such as APA, MLA or Chicago.

How to Write Research Paper

You can write Research Paper by the following guide:

  • Choose a Topic: The first step is to select a topic that interests you and is relevant to your field of study. Brainstorm ideas and narrow down to a research question that is specific and researchable.
  • Conduct a Literature Review: The literature review helps you identify the gap in the existing research and provides a basis for your research question. It also helps you to develop a theoretical framework and research hypothesis.
  • Develop a Thesis Statement : The thesis statement is the main argument of your research paper. It should be clear, concise and specific to your research question.
  • Plan your Research: Develop a research plan that outlines the methods, data sources, and data analysis procedures. This will help you to collect and analyze data effectively.
  • Collect and Analyze Data: Collect data using various methods such as surveys, interviews, observations, or experiments. Analyze data using statistical tools or other qualitative methods.
  • Organize your Paper : Organize your paper into sections such as Introduction, Literature Review, Methods, Results, Discussion, and Conclusion. Ensure that each section is coherent and follows a logical flow.
  • Write your Paper : Start by writing the introduction, followed by the literature review, methods, results, discussion, and conclusion. Ensure that your writing is clear, concise, and follows the required formatting and citation styles.
  • Edit and Proofread your Paper: Review your paper for grammar and spelling errors, and ensure that it is well-structured and easy to read. Ask someone else to review your paper to get feedback and suggestions for improvement.
  • Cite your Sources: Ensure that you properly cite all sources used in your research paper. This is essential for giving credit to the original authors and avoiding plagiarism.

Research Paper Example

Note : The below example research paper is for illustrative purposes only and is not an actual research paper. Actual research papers may have different structures, contents, and formats depending on the field of study, research question, data collection and analysis methods, and other factors. Students should always consult with their professors or supervisors for specific guidelines and expectations for their research papers.

Research Paper Example sample for Students:

Title: The Impact of Social Media on Mental Health among Young Adults

Abstract: This study aims to investigate the impact of social media use on the mental health of young adults. A literature review was conducted to examine the existing research on the topic. A survey was then administered to 200 university students to collect data on their social media use, mental health status, and perceived impact of social media on their mental health. The results showed that social media use is positively associated with depression, anxiety, and stress. The study also found that social comparison, cyberbullying, and FOMO (Fear of Missing Out) are significant predictors of mental health problems among young adults.

Introduction: Social media has become an integral part of modern life, particularly among young adults. While social media has many benefits, including increased communication and social connectivity, it has also been associated with negative outcomes, such as addiction, cyberbullying, and mental health problems. This study aims to investigate the impact of social media use on the mental health of young adults.

Literature Review: The literature review highlights the existing research on the impact of social media use on mental health. The review shows that social media use is associated with depression, anxiety, stress, and other mental health problems. The review also identifies the factors that contribute to the negative impact of social media, including social comparison, cyberbullying, and FOMO.

Methods : A survey was administered to 200 university students to collect data on their social media use, mental health status, and perceived impact of social media on their mental health. The survey included questions on social media use, mental health status (measured using the DASS-21), and perceived impact of social media on their mental health. Data were analyzed using descriptive statistics and regression analysis.

Results : The results showed that social media use is positively associated with depression, anxiety, and stress. The study also found that social comparison, cyberbullying, and FOMO are significant predictors of mental health problems among young adults.

Discussion : The study’s findings suggest that social media use has a negative impact on the mental health of young adults. The study highlights the need for interventions that address the factors contributing to the negative impact of social media, such as social comparison, cyberbullying, and FOMO.

Conclusion : In conclusion, social media use has a significant impact on the mental health of young adults. The study’s findings underscore the need for interventions that promote healthy social media use and address the negative outcomes associated with social media use. Future research can explore the effectiveness of interventions aimed at reducing the negative impact of social media on mental health. Additionally, longitudinal studies can investigate the long-term effects of social media use on mental health.

Limitations : The study has some limitations, including the use of self-report measures and a cross-sectional design. The use of self-report measures may result in biased responses, and a cross-sectional design limits the ability to establish causality.

Implications: The study’s findings have implications for mental health professionals, educators, and policymakers. Mental health professionals can use the findings to develop interventions that address the negative impact of social media use on mental health. Educators can incorporate social media literacy into their curriculum to promote healthy social media use among young adults. Policymakers can use the findings to develop policies that protect young adults from the negative outcomes associated with social media use.

References :

  • Twenge, J. M., & Campbell, W. K. (2019). Associations between screen time and lower psychological well-being among children and adolescents: Evidence from a population-based study. Preventive medicine reports, 15, 100918.
  • Primack, B. A., Shensa, A., Escobar-Viera, C. G., Barrett, E. L., Sidani, J. E., Colditz, J. B., … & James, A. E. (2017). Use of multiple social media platforms and symptoms of depression and anxiety: A nationally-representative study among US young adults. Computers in Human Behavior, 69, 1-9.
  • Van der Meer, T. G., & Verhoeven, J. W. (2017). Social media and its impact on academic performance of students. Journal of Information Technology Education: Research, 16, 383-398.

Appendix : The survey used in this study is provided below.

Social Media and Mental Health Survey

  • How often do you use social media per day?
  • Less than 30 minutes
  • 30 minutes to 1 hour
  • 1 to 2 hours
  • 2 to 4 hours
  • More than 4 hours
  • Which social media platforms do you use?
  • Others (Please specify)
  • How often do you experience the following on social media?
  • Social comparison (comparing yourself to others)
  • Cyberbullying
  • Fear of Missing Out (FOMO)
  • Have you ever experienced any of the following mental health problems in the past month?
  • Do you think social media use has a positive or negative impact on your mental health?
  • Very positive
  • Somewhat positive
  • Somewhat negative
  • Very negative
  • In your opinion, which factors contribute to the negative impact of social media on mental health?
  • Social comparison
  • In your opinion, what interventions could be effective in reducing the negative impact of social media on mental health?
  • Education on healthy social media use
  • Counseling for mental health problems caused by social media
  • Social media detox programs
  • Regulation of social media use

Thank you for your participation!

Applications of Research Paper

Research papers have several applications in various fields, including:

  • Advancing knowledge: Research papers contribute to the advancement of knowledge by generating new insights, theories, and findings that can inform future research and practice. They help to answer important questions, clarify existing knowledge, and identify areas that require further investigation.
  • Informing policy: Research papers can inform policy decisions by providing evidence-based recommendations for policymakers. They can help to identify gaps in current policies, evaluate the effectiveness of interventions, and inform the development of new policies and regulations.
  • Improving practice: Research papers can improve practice by providing evidence-based guidance for professionals in various fields, including medicine, education, business, and psychology. They can inform the development of best practices, guidelines, and standards of care that can improve outcomes for individuals and organizations.
  • Educating students : Research papers are often used as teaching tools in universities and colleges to educate students about research methods, data analysis, and academic writing. They help students to develop critical thinking skills, research skills, and communication skills that are essential for success in many careers.
  • Fostering collaboration: Research papers can foster collaboration among researchers, practitioners, and policymakers by providing a platform for sharing knowledge and ideas. They can facilitate interdisciplinary collaborations and partnerships that can lead to innovative solutions to complex problems.

When to Write Research Paper

Research papers are typically written when a person has completed a research project or when they have conducted a study and have obtained data or findings that they want to share with the academic or professional community. Research papers are usually written in academic settings, such as universities, but they can also be written in professional settings, such as research organizations, government agencies, or private companies.

Here are some common situations where a person might need to write a research paper:

  • For academic purposes: Students in universities and colleges are often required to write research papers as part of their coursework, particularly in the social sciences, natural sciences, and humanities. Writing research papers helps students to develop research skills, critical thinking skills, and academic writing skills.
  • For publication: Researchers often write research papers to publish their findings in academic journals or to present their work at academic conferences. Publishing research papers is an important way to disseminate research findings to the academic community and to establish oneself as an expert in a particular field.
  • To inform policy or practice : Researchers may write research papers to inform policy decisions or to improve practice in various fields. Research findings can be used to inform the development of policies, guidelines, and best practices that can improve outcomes for individuals and organizations.
  • To share new insights or ideas: Researchers may write research papers to share new insights or ideas with the academic or professional community. They may present new theories, propose new research methods, or challenge existing paradigms in their field.

Purpose of Research Paper

The purpose of a research paper is to present the results of a study or investigation in a clear, concise, and structured manner. Research papers are written to communicate new knowledge, ideas, or findings to a specific audience, such as researchers, scholars, practitioners, or policymakers. The primary purposes of a research paper are:

  • To contribute to the body of knowledge : Research papers aim to add new knowledge or insights to a particular field or discipline. They do this by reporting the results of empirical studies, reviewing and synthesizing existing literature, proposing new theories, or providing new perspectives on a topic.
  • To inform or persuade: Research papers are written to inform or persuade the reader about a particular issue, topic, or phenomenon. They present evidence and arguments to support their claims and seek to persuade the reader of the validity of their findings or recommendations.
  • To advance the field: Research papers seek to advance the field or discipline by identifying gaps in knowledge, proposing new research questions or approaches, or challenging existing assumptions or paradigms. They aim to contribute to ongoing debates and discussions within a field and to stimulate further research and inquiry.
  • To demonstrate research skills: Research papers demonstrate the author’s research skills, including their ability to design and conduct a study, collect and analyze data, and interpret and communicate findings. They also demonstrate the author’s ability to critically evaluate existing literature, synthesize information from multiple sources, and write in a clear and structured manner.

Characteristics of Research Paper

Research papers have several characteristics that distinguish them from other forms of academic or professional writing. Here are some common characteristics of research papers:

  • Evidence-based: Research papers are based on empirical evidence, which is collected through rigorous research methods such as experiments, surveys, observations, or interviews. They rely on objective data and facts to support their claims and conclusions.
  • Structured and organized: Research papers have a clear and logical structure, with sections such as introduction, literature review, methods, results, discussion, and conclusion. They are organized in a way that helps the reader to follow the argument and understand the findings.
  • Formal and objective: Research papers are written in a formal and objective tone, with an emphasis on clarity, precision, and accuracy. They avoid subjective language or personal opinions and instead rely on objective data and analysis to support their arguments.
  • Citations and references: Research papers include citations and references to acknowledge the sources of information and ideas used in the paper. They use a specific citation style, such as APA, MLA, or Chicago, to ensure consistency and accuracy.
  • Peer-reviewed: Research papers are often peer-reviewed, which means they are evaluated by other experts in the field before they are published. Peer-review ensures that the research is of high quality, meets ethical standards, and contributes to the advancement of knowledge in the field.
  • Objective and unbiased: Research papers strive to be objective and unbiased in their presentation of the findings. They avoid personal biases or preconceptions and instead rely on the data and analysis to draw conclusions.

Advantages of Research Paper

Research papers have many advantages, both for the individual researcher and for the broader academic and professional community. Here are some advantages of research papers:

  • Contribution to knowledge: Research papers contribute to the body of knowledge in a particular field or discipline. They add new information, insights, and perspectives to existing literature and help advance the understanding of a particular phenomenon or issue.
  • Opportunity for intellectual growth: Research papers provide an opportunity for intellectual growth for the researcher. They require critical thinking, problem-solving, and creativity, which can help develop the researcher’s skills and knowledge.
  • Career advancement: Research papers can help advance the researcher’s career by demonstrating their expertise and contributions to the field. They can also lead to new research opportunities, collaborations, and funding.
  • Academic recognition: Research papers can lead to academic recognition in the form of awards, grants, or invitations to speak at conferences or events. They can also contribute to the researcher’s reputation and standing in the field.
  • Impact on policy and practice: Research papers can have a significant impact on policy and practice. They can inform policy decisions, guide practice, and lead to changes in laws, regulations, or procedures.
  • Advancement of society: Research papers can contribute to the advancement of society by addressing important issues, identifying solutions to problems, and promoting social justice and equality.

Limitations of Research Paper

Research papers also have some limitations that should be considered when interpreting their findings or implications. Here are some common limitations of research papers:

  • Limited generalizability: Research findings may not be generalizable to other populations, settings, or contexts. Studies often use specific samples or conditions that may not reflect the broader population or real-world situations.
  • Potential for bias : Research papers may be biased due to factors such as sample selection, measurement errors, or researcher biases. It is important to evaluate the quality of the research design and methods used to ensure that the findings are valid and reliable.
  • Ethical concerns: Research papers may raise ethical concerns, such as the use of vulnerable populations or invasive procedures. Researchers must adhere to ethical guidelines and obtain informed consent from participants to ensure that the research is conducted in a responsible and respectful manner.
  • Limitations of methodology: Research papers may be limited by the methodology used to collect and analyze data. For example, certain research methods may not capture the complexity or nuance of a particular phenomenon, or may not be appropriate for certain research questions.
  • Publication bias: Research papers may be subject to publication bias, where positive or significant findings are more likely to be published than negative or non-significant findings. This can skew the overall findings of a particular area of research.
  • Time and resource constraints: Research papers may be limited by time and resource constraints, which can affect the quality and scope of the research. Researchers may not have access to certain data or resources, or may be unable to conduct long-term studies due to practical limitations.

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Types of Research Papers: Overview

A research paper is simply a piece of writing that uses outside sources. There are different types of research papers with varying purposes and expectations for sourcing.

While this guide explains those differences broadly, ask your professor about specific disciplinary conventions.

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COGST 4250 Translational Research on Decision Making

Course description.

Course information provided by the Courses of Study 2023-2024 . Courses of Study 2024-2025 is scheduled to publish mid-June.

Introductory laboratory-based course focusing on basic foundations in translational research on decision making across the lifespan. The course introduces students to hands-on applications of research skills in the context of research on decision making, spanning basic and applied research in law, medicine, behavioral economics, and policy. It focuses on such topics as human subjects protection, working with populations across the lifespan (e.g., children, seniors), database development, working with external partners and stakeholders (e.g., schools, hospitals), and basic concepts and techniques in decision research. Students participate in weekly laboratory meetings in small teams focused on specific projects as well as monthly meetings in which all teams participate. During laboratory meetings, students discuss ongoing research, plans for new studies, and interpretations of empirical findings from studies that are in progress or have been recently completed. New students work closely with experienced students and eventually work more independently. In order to fully grasp how the research projects fit into the broader field, students read relevant papers weekly and write reaction responses. Because several projects are ongoing at all times, students have the opportunity to be involved in more than one study and are assigned multiple tasks such as piloting research paradigms, subject recruitment, data collection, data analysis, and data entry. Students attend a weekly lab meeting for 1.5 hours per week, read pertinent papers, write reaction responses, and work 10.5 hours per week in the laboratory completing tasks that contribute to ongoing research studies.

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Prerequisites/Corequisites Prerequisite: HD 1150 or HD 1170 or PSYCH 1101 also HD 2830 and HD 4750 and HD 4760.

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  Regular Academic Session.   Combined with: HD 4250

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4 Credits Stdnt Opt (Letter or S/U grades)

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 5509 COGST 4250   LAB 401

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  • M 2:00pm - 4:30pm To Be Assigned
  • Aug 26 - Dec 9, 2024

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April 3, 2024

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A periodic table of primes: Research team claims that prime numbers can be predicted

by Michael Gibb, City University of Hong Kong

Huge breakthrough in prime number theory— study from City University of Hong demonstrates primes can be predicted

Both arithmetic aficionados and the mathematically challenged will be equally captivated by new research that upends hundreds of years of popular belief about prime numbers.

Contrary to what just about every mathematician on Earth will tell you, prime numbers can be predicted, according to researchers at City University of Hong Kong (CityUHK) and North Carolina State University, U.S.

The research team comprises Han-Lin Li, Shu-Cherng Fang, and Way Kuo. Fang is the Walter Clark Chair Professor of Industrial and Systems Engineering at North Carolina State University. Kuo is a Senior Fellow at the Hong Kong Institute for Advanced Study, CityU.

This is a genuinely revolutionary development in prime number theory, says Way Kuo, who is working on the project alongside researchers from the U.S. The team leader is Han-Lin Li, a Visiting Professor in the Department of Computer Science at CityUHK.

We have known for millennia that an infinite number of prime numbers, i.e., 2, 3, 5, 7, 11, etc., can be divided by themselves and the number 1 only. But until now, we have not been able to predict where the next prime will pop up in a sequence of numbers. In fact, mathematicians have generally agreed that prime numbers are like weeds: they seem just to shoot out randomly.

"But our team has devised a way to predict accurately and swiftly when prime numbers will appear," adds Kuo.

The technical aspects of the research are daunting for all but a handful of mathematicians worldwide. In a nutshell, the outcome of the team's research is a handy periodic table of primes, or the PTP, pointing the locations of prime numbers. The research is available as a working paper in the SSRN Electronic Journal .

The PTP can be used to shed light on finding a future prime, factoring an integer, visualizing an integer and its factors, identifying locations of twin primes, predicting the total number of primes and twin primes or estimating the maximum prime gap within an interval, among others.

More to the point, the PTP has major applications today in areas such as cyber security. Primes are already a fundamental part of encryption and cryptography, so this breakthrough means data can be made much more secure if we can predict prime numbers, Kuo explains.

This advance in prime number research stemmed from working on systems reliability design and a color coding system that uses prime numbers to enable efficient encoding and more effective color compression. During their research, the team discovered that their calculations could be used to predict prime numbers .

Provided by City University of Hong Kong

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Research paper assistance sites mentioned on this list are 100% safe to use, and you don’t need to worry about any negative repercussions from using their services. The most reputable sites will have a confidentiality policy, where your interaction with their research paper writers will remain anonymous. Nobody will know you have used the site unless you share this information yourself.

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Can you get caught using term paper writing services?

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Things become less clear when you consider, or intend to submit a research paper that you bought. Many sites do not encourage this, and it should not be the main reason that you look for a service to write your essay for you. You have a much higher chance of being caught for submitting a bought research paper as your own, but you may also get away with it … do so at your own risk!

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The news and editorial staff of the Delco Daily Times had no role in this post’s preparation.

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This paper is in the following e-collection/theme issue:

Published on 10.4.2024 in Vol 26 (2024)

Effectiveness of a Web-Based Individual Coping and Alcohol Intervention Program for Children of Parents With Alcohol Use Problems: Randomized Controlled Trial

Authors of this article:

Author Orcid Image

Original Paper

  • Håkan Wall 1 , PhD   ; 
  • Helena Hansson 2 , PhD   ; 
  • Ulla Zetterlind 3 , PhD   ; 
  • Pia Kvillemo 1 , PhD   ; 
  • Tobias H Elgán 1 , PhD  

1 Stockholm Prevents Alcohol and Drug Problems, Centre for Psychiatry Research, Department of Clinical Neuroscience, Karolinska Institutet, & Stockholm Health Care Services, Stockholm, Sweden

2 School of Social Work, Faculty of Social Sciences, Lund University, Lund, Sweden

3 Clinical Health Promotion Centre, Department of Health Sciences, Lund University, Lund, Sweden

Corresponding Author:

Tobias H Elgán, PhD

Stockholm Prevents Alcohol and Drug Problems, Centre for Psychiatry Research

Department of Clinical Neuroscience

Karolinska Institutet, & Stockholm Health Care Services

Norra Stationsgatan 69

Stockholm, 11364

Phone: 46 700011003

Email: [email protected]

Background: Children whose parents have alcohol use problems are at an increased risk of several negative consequences, such as poor school performance, an earlier onset of substance use, and poor mental health. Many would benefit from support programs, but the figures reveal that only a small proportion is reached by existing support. Digital interventions can provide readily accessible support and potentially reach a large number of children. Research on digital interventions aimed at this target group is scarce. We have developed a novel digital therapist-assisted self-management intervention targeting adolescents whose parents had alcohol use problems. This program aims to strengthen coping behaviors, improve mental health, and decrease alcohol consumption in adolescents.

Objective: This study aims to examine the effectiveness of a novel web-based therapist-assisted self-management intervention for adolescents whose parents have alcohol use problems.

Methods: Participants were recruited on the internet from social media and websites containing health-related information about adolescents. Possible participants were screened using the short version of the Children of Alcoholics Screening Test-6. Eligible participants were randomly allocated to either the intervention group (n=101) or the waitlist control group (n=103), and they were unblinded to the condition. The assessments, all self-assessed, consisted of a baseline and 2 follow-ups after 2 and 6 months. The primary outcome was the Coping With Parents Abuse Questionnaire (CPAQ), and secondary outcomes were the Center for Epidemiological Studies Depression Scale, Alcohol Use Disorders Identification Test (AUDIT-C), and Ladder of Life (LoL).

Results: For the primary outcome, CPAQ, a small but inconclusive treatment effect was observed (Cohen d =–0.05 at both follow-up time points). The intervention group scored 38% and 46% lower than the control group on the continuous part of the AUDIT-C at the 2- and 6-month follow-up, respectively. All other between-group comparisons were inconclusive at either follow-up time point. Adherence was low, as only 24% (24/101) of the participants in the intervention group completed the intervention.

Conclusions: The findings were inconclusive for the primary outcome but demonstrate that a digital therapist-assisted self-management intervention may contribute to a reduction in alcohol consumption. These results highlight the potential for digital interventions to reach a vulnerable, hard-to-reach group of adolescents but underscore the need to develop more engaging support interventions to increase adherence.

Trial Registration: ISRCTN Registry ISRCTN41545712; https://www.isrctn.com/ISRCTN41545712?q=ISRCTN41545712

International Registered Report Identifier (IRRID): RR2-10.1186/1471-2458-12-35

Introduction

Children who grow up with parents who have substance use problems or disorders face extraordinary challenges. Approximately 20% of all children have parents with alcohol problems [ 1 - 5 ], while approximately 5% have parents with alcohol use disorders [ 4 , 6 , 7 ]. Children growing up with parental substance abuse are at an increased risk of several negative outcomes, such as psychiatric morbidity [ 8 - 12 ]; poor intellectual, cognitive, and academic achievement [ 13 - 15 ]; domestic physical abuse [ 16 ]; and early drinking onset and the development of substance use problems [ 9 , 17 , 18 ]. Thus, children exposed to parental substance abuse comprise a target group for selective interventions and prevention strategies [ 19 - 22 ].

In Sweden, municipalities account for most of the support offered to these children. An annual survey by the junior association of the Swedish branch of Movendi International (ie, an international temperance movement) reported that 97% of all municipalities provided support resources [ 23 ]. However, estimates from the same survey showed that approximately 2% of the children in the target group received support. Hence, an overwhelming majority never receives support, mainly because of difficulties in identifying and attracting them to intervention programs [ 22 , 24 ].

The internet has become an appealing way to reach and support a large number of people [ 25 , 26 ]. Web-based interventions seem particularly attractive to adolescents, as they generally use digital technology and social media. Furthermore, research has shown that adolescents regard the internet as inviting because it is a readily accessible, anonymous way of seeking help [ 27 ]. Web-based interventions can reduce the stigma associated with face-to-face consultations in health care settings [ 28 ], and young people appreciate the flexibility of completing web-based sessions to fit their own schedules [ 29 ]. The positive effects of web-based interventions have been detected across a broad range of conditions. A recent review by Hedman-Lagerlöf et al [ 30 ] concluded that therapist-supported internet-based cognitive behavioral therapy for adults yielded similar effects as face-to-face therapy. To date, most web-based interventions have been designed for adults. Although the number of web-based interventions targeting children or adolescents is increasing [ 25 , 31 - 33 ], the number of digital interventions aimed at children of substance-abusing parents is still scarce [ 22 , 34 - 38 ]. Those described in the literature, however, all have in common that they are quite extensive, with a duration over several weeks, and a brief digital intervention could complement these more extended interventions. For instance, our research group initiated a study on a web-based group chat for 15- to 25-year-old individuals who have parents with mental illness or substance use problems [ 35 ]. The duration of the program is 8 weeks, and it is a translated version of a program from the Netherlands [ 34 ], which has been shown to have inconclusive treatment effects [ 39 ]. In Sweden, 2 other programs with inconclusive treatment effects have been tested that target significant others and their children [ 37 , 38 ]. Finally, a digital intervention developed in Australia for 18- to 25-year-old individuals with parents with mental illness or substance use disorder [ 36 ] was tested in a pilot study demonstrating positive findings [ 40 ].

To meet the need for a brief, web-based intervention that targets adolescents having parents with alcohol problems and build on the evidence base of digital interventions targeting this vulnerable group, we developed a novel internet-delivered therapist-assisted self-management intervention called “Alcohol and Coping.” Our program originated from a manual-based face-to-face intervention called the “Individual Coping and Alcohol Intervention Program” (ICAIP) [ 41 , 42 ]. Previous studies on both the ICAIP, which aimed at college students having parents with alcohol problems, and a coping skills intervention program, which aimed at spouses of partners with alcohol dependency [ 43 ], have demonstrated positive effects regarding decreased alcohol consumption and improved mental health and coping behaviors [ 41 - 44 ]. Furthermore, the results from these studies underscore the importance of improving coping skills [ 42 , 44 ]. Among college students, those who received a combination of coping skills and an alcohol intervention program had better long-term outcomes [ 42 ].

The aim of this study was to test the effectiveness of Alcohol and Coping among a sample of adolescents aged 15-19 years with at least 1 parent with alcohol use problems. We hypothesized that the intervention group would be superior to the control group in improving coping skills. Secondary research questions concerned the participants’ improvement in (1) depression, (2) alcohol consumption, and (3) quality of life.

This study was a parallel-group randomized controlled trial in which participants were randomized to either the intervention or waitlist control group in a 1:1 allocation ratio. The trial design is illustrated in Figure 1 .

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Recruitment and Screening

The participants were recruited from August 2012 to December 2013 through advertisements on social media (Facebook). The advertisements targeted individuals aged 15-19 years with Facebook accounts. Participants were recruited on the internet through advertisements on websites containing health-related information about adolescents. The advertisements included the text, “Do your parents drink too much? Participate in a study.” The advertisement contained an invitation to perform a web-based, self-assessed screening procedure. In addition to questions about age and sex, participants were screened for having parents with alcohol problems using the short version of the Children of Alcoholics Screening Test-6 (CAST-6), developed from a 30-item original version [ 45 ]. The CAST-6 is a 6-item true-false measure designed to assess whether participants perceive their parents’ alcohol consumption to be problematic. The CAST-6 has demonstrated high internal consistency ( r =0.92-0.94), test-retest reliability ( r =0.94), and high validity as compared to the 30-item version ( r =0.93) using the recommended threshold score of 3 or higher [ 45 , 46 ]. We previously translated the CAST-6 into Swedish and validated the translated version among 1450 adolescents, showing good internal consistency (α=.88), excellent test-retest reliability (intraclass correlation coefficient=0.93), and loading into 1 latent factor [ 47 ]. Additional inclusion criteria included having access to a computer and the internet and being sufficiently fluent in Swedish. Participants were excluded from the study and were referred to appropriate care if there were indications of either suicidal or self-inflicted harmful behaviors. Individuals eligible for inclusion received further information about the study and were asked to provide consent to participate by providing an email address.

Data Collection and Measures

All assessments were administered through email invitations containing a hyperlink to the web-based self-reported assessments. Up to 3 reminders were sent through email at 5, 10, and 15 days after the first invitation. A baseline assessment (t 0 ) was collected before randomization, and follow-up assessments were conducted at 2 and 6 months (t 1 and t 2 , respectively) after the initial assessment.

Participants were asked for age, sex, whether they lived with a parent (mother and father, mother or father, mother or father and stepparent, or alternate between mother and father), where their parents were born (Sweden or a Nordic country excluding Sweden or outside of the Nordic countries), parental status (employed, student, on parental leave, or unemployed), and any previous or present participation in support activities for children having parents with alcohol use problems. The primary outcome was coping, measured using the Coping With Parents Abuse Questionnaire (CPAQ) based on the Coping Behavior Scale developed by Orford et al [ 48 ]. Secondary outcomes were the Center for Epidemiological Studies Depression Scale (CES-DC) [ 49 ], the 3-question Alcohol Use Disorders Identification Test (AUDIT-C) [ 50 ], and the Ladder of Life (LoL), which measures the overall quality of life by asking about the participants’ past, present, and future ratings of their overall life satisfaction [ 50 ]. CPAQ has been shown to be reliable [ 41 , 42 ]. For this study, this scale was factor-analyzed to reduce the number of questions from 37 to 20. The resulting scale measures 6 coping typologies (discord, emotion, control, relationship, avoidance, and taking specific action) using a 4-point Likert scale, with a threshold score above 50 points (out of 80) indicating dysfunctional coping behavior. The CES-DC measures depressive symptoms during the past week using a 4-point Likert scale, where a higher total score indicates more depressive symptoms [ 49 ]. A cutoff score of ≥16 indicates symptoms of moderate depression, while a score of ≥30 indicates symptoms of severe depression [ 51 , 52 ]. The scale measures 4 dimensions of depression: depressed mood, tiredness, inability to concentrate, and feelings of being outside and lonely, and has positively stated items [ 52 ]. Additionally, this scale is a general measure of childhood psychopathology [ 53 ] and has been demonstrated to be reliable and valid among Swedish adolescents [ 52 ]. Alcohol consumption was measured using a modified AUDIT-C, which assesses the frequency of drinking, quantity consumed on a typical occasion, and frequency of heavy episodic drinking (ie, binge drinking) [ 50 ] using a 30-day perspective (as opposed to the original 12-month perspective). These questions have previously been translated into Swedish [ 54 ], and a score of ≥4 and ≥5 points for women and men, respectively, was used as a cutoff for risky drinking. This scale has been demonstrated to be reliable and valid for Swedish adolescents [ 55 ]. Furthermore, 2 questions were added concerning whether the participants had ever consumed alcohol to the point of intoxication and their age at the onset of drinking and intoxication. The original version of the LoL was designed for adults and asked the respondents to reflect on their, present, and future life status from a 5-year perspective on a 10-point Visual Analogue Scale representing life status from “worst” to “best” possible life imaginable [ 56 ]. A modified version for children, using a time frame of 1 year, has been used previously in Sweden [ 57 ] and was used in this study.

Randomization

After completing the baseline assessment, each participant was allocated to either the intervention or the control group. An external researcher generated an unrestricted random allocation sequence using random allocation software [ 58 ]. Neither the participants nor the researchers involved in the study were blinded to group allocation.

Based on the order in which participants were included in the study, they were allocated to 1 of the 2 study groups and informed of their allocation by email. Additionally, those who were randomized to the intervention group received a hyperlink to the Alcohol and Coping program, whereas the control group participants received information that they would gain access to Alcohol and Coping after the last follow-up assessment (ie, the waitlist control group). All participants were informed about other information and support available through web pages, notably drugsmart [ 59 ], which contains general information and facts about alcohol and drugs, in addition to more specific information about having substance-abusing parents. Telephone numbers and contact information for other organizations and primary health care facilities were also provided.

The Intervention

As noted previously, Alcohol and Coping is derived from the aforementioned manual-based face-to-face ICAIP intervention program [ 41 , 42 ]. The ICAIP consists of a combination of an alcohol intervention program, which is based on the short version of the Brief Alcohol Screening and Intervention for College Students program [ 60 ], and a coping intervention program developed for the purpose of the ICAIP [ 41 , 42 ]. Like the original ICAIP intervention, Alcohol and Coping builds on psychoeducational principles and includes components such as film-based lectures, various exercises, and both automated and therapist-assisted feedback. Briefly, once the participants logged into the Alcohol and Coping platform, they were introduced to the program, which followed the pattern of a board game ( Figure 2 ). Following the introduction, participants took part in 3 film-based lectures (between 8 and 15 minutes each, Figure 3 ) concerning alcohol problems within the family. The respective lectures included information about (1) dependency in general as well as the genetic and environmental risks for developing dependency, (2) family patterns and how the family adapts to the one having alcohol problems, and (3) attitudes toward alcohol and how they influence drinking and the physiological effects of alcohol. After completing the lectures, the participants were asked to answer 2 questions about their own alcohol consumption (ie, how often they drink and how often they drink to intoxication), followed by an automatic feedback message that depended on their answers. It was then suggested that the participants log out of the intervention for a 1- to 2-day break. The reason for this break was to give the participants a chance to digest all information and impressions. When they logged back into the intervention, they were asked to answer 20 questions about their coping strategies, which were also followed by automatic feedback. This feedback comprised a library covering all the prewritten feedback messages, each of which was tailored to the participants’ specific answers. The participants then participated in a 5-minute–long film-based lecture on emotion and problem-focused coping in relation to family alcohol problems ( Figure 3 ). This was followed by 4 exercises where the participants read through vignette-like stories from 4 fictional persons describing their everyday lives related to coping and alcohol problems in the family. The stories are presented by film-based introductions that are each 1-2 minutes long. Participants were then requested to respond to each story by describing how the fictive person could have coped with their situation. As a final exercise, participants were asked to reflect on their own family situation and how they cope with situations. The participants then had to take a break for a few days.

During the break, a therapist composed individual feedback that covered reflections and confirmation of the participant’s exercises and answers to questions and included suggestions on well-suited coping strategies. Additionally, the therapist encouraged the participants to talk to others in their surroundings, such as friends, teachers, or coaches, and seek further support elsewhere, such as from municipal social services, youth health care centers, or other organizations. Finally, the therapist reflected on the participants’ alcohol consumption patterns and reminded them of increased genetic and environmental risks. Those who revealed patterns of risky alcohol use were encouraged to look at 2 additional film-based lectures with more information about alcohol and intoxication (4 minutes) and alcohol use and dependency (5 minutes). Participants received this feedback once they logged back into the program, but they also had the opportunity to receive feedback through email. The total estimated effective time for completing the program was about 1 hour, but as described above, there was 1 required break when the individualized feedback was written. To keep track of the dose each participant received, each of the 15 components in the program ( Figure 1 ) is equal to completing 6.7% (1/15) of the program in total.

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Sample Size

The trial was designed to detect a medium or large effect size corresponding to a standardized mean difference (Cohen d >0.5) [ 61 ]. An a priori calculation of the estimated sample size, using the software G*Power (G*Power Team) [ 62 ], revealed that a total of 128 participants (64 in each group) were required to enroll in the trial (power=0.80; α=.05; 2-tailed). However, to account for an estimated attrition rate of approximately 30% [ 34 ], it was necessary to enroll a minimum of 128/(1 – 0.3) = 183 participants in the trial. After a total of 204 individuals had been recruited and randomized into 2 study arms, recruitment was ended.

Statistical Analysis

Data were analyzed according to the intention-to-treat (ITT) principle, and all randomized participants were included, irrespective of whether they participated in the trial. The 4 research variables were depression (CES-DC), coping (CPAQ), alcohol use (AUDIT-C), and life status (LoL).

Data analysis consisted of comparing outcome measurements at t 1 and t 2 . The baseline measurement t 0 value was added as an adjustment variable in all models. The resulting data from CPAQ, CES-DC, and LoL were normally distributed and analyzed using linear mixed models. The resulting AUDIT-C scores were nonnormally distributed, with an excess of 0 values, and were analyzed using a 2-part model for longitudinal data. This model is sufficiently flexible to account for numerous 0 reports. This was achieved by combining a logistic generalized linear mixed model (GLMM) for the 0 parts and a skewed continuous GLMM for the non-0 alcohol consumption parts. R-package brms (Bayesian regression models using Stan; R Foundation for Statistical Computing) [ 63 ], a higher-level interface for the probabilistic programming language Stan [ 64 ], and a custom brms family for a marginalized 2-part lognormal distribution were used to fit the model [ 65 ]. The logistic part of the model represents the subject-specific effects on the odds of reporting no drinking. The continuous part was modeled using a gamma GLMM with a log link. The exponentiated treatment effect represents the subject-specific ratio of the total AUDIT-C scores between the treatment and waitlist control groups for those who reported drinking during the specific follow-up period.

Handling of Missing Data

GLMMs include all available data and provide unbiased ITT estimates under the assumption that data are missing at random, meaning that the missing data can be explained by existing data. However, it is impossible to determine whether the data are missing at random or whether the missing data are due to unobserved factors [ 66 ]. Therefore, we also assumed that data were not missing at random, and subsequent sensitivity analyses were performed [ 66 ]. We used the pattern mixture method, which assumes not missing at random, to compare those who completed the follow-up at 6 months (t 2 ) with those who did not (but completed the 2-month follow-up). The overall effect of this model is a combination of the effects of each subgroup. We also tested the robustness of the results by performing ANCOVAs at the 2-month follow-up, both using complete cases and with missing values imputed using multilevel multiple imputation.

The effect of the program was estimated using Cohen d , where a value of approximately 0.2 indicates a small effect size and values of approximately 0.5 and 0.8 indicate medium and large effect sizes, respectively [ 61 ].

Ethical Considerations

All procedures were performed in accordance with the ethical standards of the institutional or national research committees, the 1964 Helsinki Declaration and its later amendments, and comparable ethical standards. Informed consent was obtained from all the participants included in the study. This study was approved by the Swedish Ethical Review Authority (formerly the Regional Ethical Review Board in Stockholm, No. 2011/1648-31/5).

To enhance the response rates, participants received a cinema gift certificate corresponding to approximately EUR 11 (US $12) as compensation for completing each assessment. If a participant completed all assessments, an additional gift certificate was provided. The participants could subsequently receive 4 cinema gift certificates totaling EUR 44 (US $48).

The trial profile is depicted in Figure 1 and reveals that 2722 individuals who were aged between 15 and 19 years performed the screening procedure. A total of 1448 individuals did not fulfill the inclusion criteria and were excluded, leaving 1274 eligible participants. Another 1070 individuals were excluded because they did not provide informed consent or complete the baseline assessment, leaving 204 participants who were allocated to 1 of the 2 study groups. A total of 140 (69%) and 131 (64%) participants completed t 1 and t 2 assessments, respectively. Of the participants in the intervention group (n=101), 63% (n=64) registered an account on the Alcohol and Coping website, 35% (n=35) completed the alcohol intervention section, and 24% (n=24) completed both the alcohol and coping intervention sections.

Sample Characteristics

The mean age of the sample was 17.0 (SD 1.23) years, and the vast majority were female, with both parents born in Sweden and currently working ( Table 1 ). Approximately one-third of the participants reported living with both parents. The mean score on the CAST-6 was 5.33 (SD 0.87) out of a total of 6, and the majority of the sample (147/204, 72.1%) perceived their father to have alcohol problems. Approximately 12% (25/204) had never consumed alcohol, whereas approximately 70% (144/204) had consumed alcohol at a level of intoxication. The mean age at onset was 13.7 (SD 2.07) years and the age at first intoxication was 14.8 (SD 1.56) years. The proportion of participants with symptoms of at least moderate depression was 77.5% (158/204), of whom 55.1% (87/158) had symptoms of severe depression and 42.6% (87/204) had symptoms of dysfunctional coping behaviors. The percentage of participants who consumed alcohol at a risky level was 39.7% (81/204). Table 1 provides complete information regarding the study sample.

a Significance levels calculated by Pearson chi-square statistics for categorical variables and 2-tailed t tests for continuous variables.

Treatment Effects

For the primary outcome, coping behavior (CPAQ), we found a small but inconclusive treatment effect in favor of treatment at both 2 (t 1 ) and 6 (t 2 ) months (Cohen d =–0.05 at both t 1 and t 2 ). For the secondary outcome, alcohol use (AUDIT-C), we found a treatment effect in that the intervention group scored 38% less than the control group on the continuous part (ie, drinking when it occurred) at t 1 and 46% less at t 2 . Regarding depression (CES-DC) and life status (LoL), all between-group comparisons of treatment effects were inconclusive at both follow-up time points ( Table 2 ).

a CPAQ: Coping With Parents Abuse Questionnaire.

b CES-DC: Center for Epidemiological Studies Depression Scale.

c LoL: Ladder of Life.

d AUDIT-C: Alcohol Use Disorders Identification Test.

e N/A: not applicable.

Missing Data

In contrast to the ITT analyses, the sensitivity analyses showed that the treatment group, averaged over the levels of dropout, scored higher (ie, a negative effect) on the main outcome, coping behavior (CPAQ), at t 1 (2.44; P =.20). However, the results remain inconclusive.

Dose-Response Effects

We did not find any evidence for greater involvement in the program being linked to improved outcomes with regard to coping behavior.

We did not find any support for the primary hypothesis: the intervention was not superior to the control condition with regard to coping behavior. Inconclusive results with small effect sizes were observed at both follow-up time points. However, for the secondary outcomes, we found that those in the intervention group who drank alcohol drank approximately 40%-50% less than those in the control group at both follow-ups. These results corroborate previous findings on the precursor face-to-face ICAIP intervention program, demonstrating that participants who received a combined alcohol and coping intervention reported superior outcomes with regard to alcohol-related outcomes compared to participants in the other 2 study arms, who received only a coping or alcohol intervention [ 41 , 42 ]. In contrast to this study, Hansson et al [ 42 ] found that all groups improved their coping skills, although the between-group comparisons were inconclusive and the improvements were maintained over time. These differences could be explained by the different settings in which the precursor program was provided (ie, face-to-face to young adults in a university setting), whereas this study targeted young people (15-19 years of age) through a web-based digital intervention. Additionally, the poor adherence in this study may explain the absence of primary results favoring the intervention group. In a recent study, parents without alcohol problems were recruited to participate in a randomized trial evaluating the web-based SPARE (Supportive Parenting and Reinforcement) program to improve children’s mental health and reduce coparents’ alcohol use. In line with our study, the authors did not find the primary outcome of the SPARE program to be superior to that of the active control group (which received written psychoeducation); however, both groups reported decreased coparental alcohol consumption [ 38 ].

Considering that approximately 3600 children in 2022 participated in various forms of support provided by Swedish municipalities [ 23 ], our recruitment activities reached a large number of eligible individuals, pointing to the potential of finding these children on these platforms. There were unexpectedly high levels of depression among the participants in this study. Although the intervention did not target depressive symptoms per se , there was a trend for the intervention group to have decreased depression levels compared to the control group. A large proportion of participants had symptoms of severe depression, which may have aggravated their capacity for improvement at follow-up [ 28 , 67 ]. Targeting dysfunctional coping patterns could affect an individual’s perceived mental health, and studies have shown that healthy coping strategies positively affect depression and anxiety in a positive way [ 68 ]. Using dysfunctional coping strategies, such as negative self-talk and alcohol consumption, can lead to depressive symptoms [ 69 ]. Targeting these symptoms in the context of healthy and unhealthy coping strategies may be a viable route to fostering appropriate coping strategies that work in the long run. Given that the young people who were reached by the intervention in this study displayed high levels of depression, future interventions for this group should include programs targeting depressive symptoms.

Almost 37% (37/101) of the intervention group did not log into the intervention at all, and only 24% (24/101) of the intervention group participants completed all parts of the program. The fact that a high proportion of the participants had symptoms of severe depression could explain the low adherence. Another reason could be that the initial film-based lectures were too long to maintain the participants’ attention, as the lectures ranged from 8-15 minutes. Yet a final reason could be that we had a 1- to 2-day break built into the intervention, and for unknown reasons, some participants did not log back into the intervention. However, we did not find a dose-response relationship indicating favorable outcomes for those who completed more of the program content. High levels of attrition are not uncommon in self-directed programs such as the one in this study; for example, in a study on a smoking cessation intervention, 37% of the participants never logged into the platform [ 70 ], and in a self-directed intervention for problem gamblers, a majority dropped out after 1 week and none completed the entire program [ 71 ]. Increased intervention adherence is a priority when developing new digital interventions, particularly for young people. One method is to use more persuasive technologies, such as primary tasks, dialogue, and social support [ 72 ]. Considering children whose parents have mental disorders, Grové and Reupert [ 73 ] suggested that digital interventions should include components such as providing information about parental mental illness, access to health care, genetic risk, and suggestions for how children might initiate conversations with parents who have the illness. These suggestions should be considered in future studies on interventions for youths whose parents have substance use problems. Representatives of the target group and other relevant stakeholders should also be involved in coproducing new interventions to increase the probability of developing more engaging programs [ 74 ]. Moreover, one cannot expect study participants to return to the program more than once, and for the sake of adherence, briefer interventions should not encourage participants to log-out for a break. To keep adherence at an acceptable level, similar future interventions for this target group should also consider having symptoms of severe depression as an exclusion criterion [ 28 , 67 ]. Further, to improve adherence, strategies of coproduction could be used where all stakeholders, including the target group, are involved in intervention development [ 75 ]. Other important factors identified to improve adherence to digital interventions are to make the content relatable, useful, and even more interactive [ 76 ]. Those participants who have symptoms of severe depression should be referred to other appropriate health care. Finally, it is probably beneficial to develop shorter psychoeducative film-based lectures than ours, lasting up to 15 minutes. Future self-directed digital interventions targeting this population should, therefore, focus on a very brief and focused intervention, which, based on theory, has the potential to foster healthy coping behaviors that can lead to an increased quality of life and improved mental health for this group of young people.

Another concern for future projects would be to use a data-driven approach during the program development phase, where A/B testing can be used to test different setups of the program to highlight which setup works best. Another aspect that must be considered is the fast-changing world of technology, where young people are exposed to an infinite number of different apps that grab their attention, which also calls for interventions to be short and to the point. Furthermore, if the program is to spread and become generally available, one must consider that keeping the program alive for a longer period will require funding and staffing for both product management and technical support.

Strengths and Limitations

This study had several strengths. First, Alcohol and Coping is a web-based intervention program, and it appears as if the internet is a particularly promising way to provide support to adolescents growing up with parents with alcohol problems because it offers an anonymous means of communicating and makes intervention programs readily accessible [ 25 ]. Our recruitment strategies reached a considerable number of interested and eligible individuals, demonstrating the potential for recruiting through social media and other web platforms. Additionally, this program is one of the first brief web-based interventions aimed at adolescents with parents with alcohol-related problems. We used the CAST-6, which has been validated among Swedish adolescents [ 47 ], to screen eligible participants. Another strength is that the intervention program involved personalized, tailored feedback in the form of prewritten automatic messages and therapist-written personalized feedback, both of which have proven to be important components of web-based interventions aimed at adolescents [ 77 , 78 ]. Finally, this study evaluated the effectiveness of the Alcohol and Coping program using a randomized controlled trial design, which is considered the strongest experimental design with regard to allocation bias.

This study had some limitations. First, the design with a passive waitlist control group and an active intervention group, both unblinded to study allocation, may have resulted in biased estimates of treatment effects. Intervention adherence was low, and most of the study participants had symptoms of depression, where 55% (87/158) had symptoms of severe depression. This may have contributed to the small and overall inconclusive effects on the primary outcomes of this study. Many digital interventions have problems with low adherence, and in a review by Välimäki et al [ 79 ], some studies reported adherence rates as low as 10%. A vast proportion of the study participants were women, making the findings difficult to generalize to men. However, another limitation concerns selection bias and external validity. We recruited study participants through social media and other relevant websites containing health-related information, including information about parents with alcohol-related problems. It is, therefore, possible that the study population can be classified as “information-seeking” adolescents, who may have different personality traits relative to other adolescents in the same home situation. Additionally, as an inclusion criterion was having ready access to computers and the internet, it is possible that participants belonging to a lower socioeconomic class were underrepresented in the study. It should also be noted that the data presented here were collected approximately 10 years ago. However, we believe our findings make an important contribution to the field since, like our intervention, many recent web-based interventions use strategies of psychoeducation, films, exercises, questions, and feedback. Further, the number of web-based interventions for this target group remains scarce in the literature, which underscores the need for future research. Finally, the study was powered to detect a medium effect size. However, given the small effect sizes detected in this study, it is plausible that too few participants were recruited to detect differences between the groups.

Implications for Practice

Although growing up with parents who have alcohol problems per se is not sufficient for developing psychosocial disorders, many children need support to manage their situation. Therefore, it is difficult to recruit children to support these groups. In Sweden, not even 2% of all children growing up with parental alcohol problems attend face-to-face support groups provided by municipalities.

Offering support through web-based intervention programs seems particularly attractive to adolescents whose parents have alcohol-related problems. To date, evidence for such programs is scarce, and there is an urgent need to develop and evaluate digital interventions targeting this group of adolescents. This study makes important contributions to this novel field of research. The results provide insight into effective strategies for delivering intervention programs to children of parents with substance abuse issues, highlighting the potential for digital interventions to reach a vulnerable, hard-to-reach group of adolescents. Our findings underscore the need to develop more engaging interventions in coproduction with the target group.

Conclusions

We found that a digital therapist-assisted self-management intervention for adolescents whose parents have alcohol use problems contributed to a reduction in the adolescents’ own alcohol consumption. This result highlights the potential for digital interventions to reach a large, vulnerable, and hard-to-reach group of adolescents with support efforts. Findings were inconclusive for all other outcomes, which may be attributable to low adherence. This points to the need for future research on developing more engaging digital interventions to increase adherence among adolescents.

Acknowledgments

This work was undertaken on behalf of the Swedish Council for Information on Alcohol and Other Drugs (CAN) and was supported by grants from the Swedish National Institute of Public Health and the Swedish Council for Working Life and Social Research.

Conflicts of Interest

HH and UZ developed the study interventions. However, the parties did not derive direct financial income from these interventions. HW, PK, and THE declare no conflicts of interest.

CONSORT-eHEALTH checklist (V 1.6.1).

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Abbreviations

Edited by YH Lin; submitted 24.08.23; peer-reviewed by X Zhang, C Asuzu, D Liu; comments to author 28.01.24; revised version received 08.02.24; accepted 27.02.24; published 10.04.24.

©Håkan Wall, Helena Hansson, Ulla Zetterlind, Pia Kvillemo, Tobias H Elgán. Originally published in the Journal of Medical Internet Research (https://www.jmir.org), 10.04.2024.

This is an open-access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work, first published in the Journal of Medical Internet Research, is properly cited. The complete bibliographic information, a link to the original publication on https://www.jmir.org/, as well as this copyright and license information must be included.

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Angry young white woman sitting at a desk. She is wearing a green shirt and jeans and is stretching out her hands and scrunching her eyes shut in frustration.

Write down your thoughts and shred them to relieve anger, researchers say

Writing negative reactions on paper and shredding it or scrunching and throwing in the bin eliminates angry feelings, study finds

Since time immemorial humans have tried to devise anger management techniques.

In ancient Rome, the Stoic philosopher Seneca believed “my anger is likely to do me more harm than your wrong” and offered avoidance tips in his AD45 work De Ira (On Anger).

More modern methods include a workout on the gym punchbag or exercise bike. But the humble paper shredder may be a more effective – and accessible – way to decompress, according to research.

A study in Japan has found that writing down your reaction to a negative incident on a piece of paper and then shredding it, or scrunching it into a ball and throwing it in the bin, gets rid of anger.

“We expected that our method would suppress anger to some extent,” said Nobuyuki Kawai, lead researcher of the study at Nagoya University. “However, we were amazed that anger was eliminated almost entirely.”

The study, published in Scientific Reports on Nature , builds on research on the association between the written word and anger reduction as well as studies showing how interactions with physical objects can control a person’s mood. For instance, those wanting revenge on an ex-partner may burn letters or destroy gifts.

Researchers believe the shredder results may be related to the phenomenon of “backward magical contagion”, which is the belief that actions taken on an object associated with a person can affect the individuals themselves. In this case, getting rid of the negative physical entity, the piece of paper, causes the original emotion to also disappear.

This is a reversal of “magical contagion” or “celebrity contagion” – the belief that the “essence” of an individual can be transferred through their physical possessions.

Fifty student participants were asked to write brief opinions about an important social problem, such as whether smoking in public should be outlawed. Evaluators then deliberately scored the papers low on intelligence, interest, friendliness, logic, and rationality. For good measure, evaluators added insulting comments such as: “I cannot believe an educated person would think like this. I hope this person learns something while at the university.”

The wound-up participants then wrote down their angry thoughts on the negative feedback on a piece of paper. One group was told to either roll up the paper and throw it in a bin or keep it in a file on their desk. A second group was told to shred the paper, or put it in a plastic box.

Anger levels of the individuals who discarded their paper in the bin or shredded it returned to their initial state, while those who retained a hard copy of the paper experienced only a small decrease in their overall anger.

Researchers concluded that “the meaning (interpretation) of disposal plays a critical role” in reducing anger.

“This technique could be applied in the moment by writing down the source of anger as if taking a memo and then throwing it away,” said Kawai.

Along with its practical benefits, this discovery may shed light on the origins of the Japanese cultural tradition known as hakidashisara ( hakidashi sara refers to a dish or plate) at the Hiyoshi shrine in Kiyosu, just outside Nagoya. Hakidashisara is an annual festival where people smash small discs representing things that make them angry. The study’s findings may explain the feeling of relief that participants report after leaving the festival, the paper concluded.

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One Hundred Years and Counting: The International Growth of Waldorf Education

Teaching Children to Write and Read in Waldorf Schools Provisionally Accepted

  • 1 Steiner Education Development Trust, New Zealand

The final, formatted version of the article will be published soon.

A well-established principle of Waldorf Education is that children's development is compromised if we bring intellectual teaching too early. Waldorf teachers congratulate themselves that they wait until the seventh year to begin formal schooling, but according to the principles out of which Waldorf Education arose, teaching children to read and write at seven is not ideal; they are still not ready.Convention and state expectations made it necessary in 1919 to introduce literacy at an age close to what was considered normal, so a compromise was needed. Steiner suggested that, because physical development reaches a certain completion at seven, it is less harmful if we wait until then, but this was still a compromise: we cannot unleash any kind of teaching scheme on seven-year-olds without doing any harm. According to modern teaching principles, starting earlier means getting ahead; everything should be taught explicitly and nothing left to develop of its own accord. 1 Proponents of synthetic phonics refer to research showing that it produces the best results 2 , which is why it has been adopted so widely in mainstream education. However, the validity of this claim depends on what we mean by 'better results' and 'literacy'. This paper explores these ideas.1 Ken Robinson, Out of Our Minds: The Power of Being Creative (2017) Capstone Press, Mankato Minnesota 2 A longitudinal study reported by Johnston and Watson (2005) found that a group taught by synthetic phonics had better spelling, word reading and comprehension than a group taught by analytic phonics.

Keywords: Waldorf education, Literacy in Waldorf schools, Steiner education, Teaching literacy, Teaching literacy through art, Teaching reading and writing, Adaptive teaching

Received: 19 Feb 2024; Accepted: 10 Apr 2024.

Copyright: © 2024 Bell. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Mx. Amanda Bell, Steiner Education Development Trust, Wellington, New Zealand

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  1. APA Style Guidelines for Numbers

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  4. PDF 7th Edition Numbers and Statistics Guide

    Numbers and Statistics Guide Numbers see Publication Manual Sections 6.32-6.35 for guidelines on using numerals vs. words • Use numerals (1, 2, 3, etc.) for the following: ° numbers 10 and above; see exceptions in the next section ° numbers used in statistics (e.g., 2.45, 3 times as many, 2 x 2 design) ° numbers used with units of ...

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  9. Reporting Statistics in APA Style

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  10. Academic Guides: Other APA Guidelines: Numbers

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  12. Numbers

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  13. Numbers In Academic Writing ~ APA Style Guidelines

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  14. Numbers in Scientific Manuscripts: What Are the Rules?

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  17. PDF Student Paper Setup Guide, APA Style 7th Edition

    Indent the first line of every paragraph of text 0.5 in. using the tab key or the paragraph-formatting function of your word-processing program. Page numbers: Put a page number in the top right corner of every page, including the title page or cover page, which is page 1. Student papers do not require a running head on any page.

  18. How to Write a Research Paper

    This interactive resource from Baylor University creates a suggested writing schedule based on how much time a student has to work on the assignment. "Research Paper Planner" (UCLA) UCLA's library offers this step-by-step guide to the research paper writing process, which also includes a suggested planning calendar.

  19. Q: How to write large numbers in a research paper?

    1 Answer to this question. Answer: While writing numbers in a research paper, it is best practice to write small numbers from one to ten in words and bigger numbers in figures, for the ease of reading. Moreover, it also depends on the style guide you are using. For example, the APA style guide recommends writing small numbers from one to nine ...

  20. Research Paper

    Definition: Research Paper is a written document that presents the author's original research, analysis, and interpretation of a specific topic or issue. It is typically based on Empirical Evidence, and may involve qualitative or quantitative research methods, or a combination of both. The purpose of a research paper is to contribute new ...

  21. How to Start Getting Published in Medical and Scientific Journals

    "In terms of publishing academic research, the number-one holdup in my position right now is a lack of scientific writers," says Jessica Lasky-Su, DSc, MS, associate professor in medicine and associate statistician at Harvard Medical School and Brigham and Women's Hospital, and faculty for the Effective Writing for Health Care certificate ...

  22. Overview

    A research paper is simply a piece of writing that uses outside sources. There are different types of research papers with varying purposes and expectations for sourcing. While this guide explains those differences broadly, ask your professor about specific disciplinary conventions. To argue for a single claim or thesis through evidence and ...

  23. Class Roster

    About the Class Roster. Fall 2024 - COGST 4250 - Introductory laboratory-based course focusing on basic foundations in translational research on decision making across the lifespan. The course introduces students to hands-on applications of research skills in the context of research on decision making, spanning basic and applied research in law ...

  24. A periodic table of primes: Research team claims that prime numbers can

    We have known for millennia that an infinite number of prime numbers, i.e., 2, 3, 5, 7, 11, etc., can be divided by themselves and the number 1 only. But until now, we have not been able to ...

  25. Best Research Paper Writing Services: Top 5 U.S. Companies

    1. PaperHelp: Best Research Paper Writing Service Overall. On all of the factors that we judged these 5 paper writing services by, PaperHelp consistently impressed on all fronts. With prices ...

  26. Journal of Medical Internet Research

    This paper is in the following e-collection/theme issue: Web-based and Mobile Health Interventions (2944) Registered Report (472) Alcohol Abuse, Alcoholism Prevention and Recovery (279) Formative Evaluation of Digital Health Interventions (2052) Substance Abuse (351) Prevention and Health Promotion (787) Interventions and Support for Informal Caregivers of People with Mental Illness (85)

  27. Write down your thoughts and shred them to relieve anger, researchers

    A study in Japan has found that writing down your reaction to a negative incident on a piece of paper then shredding it, or scrunching it into a ball and throwing it in the bin, gets rid of anger ...

  28. Teaching Children to Write and Read in Waldorf Schools

    A well-established principle of Waldorf Education is that children's development is compromised if we bring intellectual teaching too early. Waldorf teachers congratulate themselves that they wait until the seventh year to begin formal schooling, but according to the principles out of which Waldorf Education arose, teaching children to read and write at seven is not ideal; they are still not ...