{"id":306043,"date":"2021-04-01T18:15:34","date_gmt":"2021-04-01T16:15:34","guid":{"rendered":"https:\/\/www.scribbr.nl\/?p=306043"},"modified":"2023-10-03T10:05:09","modified_gmt":"2023-10-03T08:05:09","slug":"numbers-and-statistics","status":"publish","type":"post","link":"https:\/\/www.scribbr.com\/apa-style\/numbers-and-statistics\/","title":{"rendered":"Reporting Statistics in APA Style | Guidelines &#038; Examples"},"content":{"rendered":"<p>The <a href=index-1778.html><em>APA Publication Manual<\/em><\/a> 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.<\/p>\n<p><a href=indexaa2a.html?cat_ID=34372\%22>Statistical analysis<\/a> involves gathering and testing <a href=index-2992.html>quantitative data<\/a> to make inferences about the world. A <a href=index-3026.html>statistic<\/a> is any number that describes a <a href=index-2997.html>sample<\/a>: it can be a proportion, a <a href=index-3022.html>range<\/a>, or a measurement, among other things.<\/p>\n<p>When reporting statistics, use these formatting rules and suggestions from APA where relevant.<\/p>\n<p><!--more--><\/p>\n<h2>Numbers and measurements<\/h2>\n<p>In general, <a href=index-4640.html#numbers\">APA advises using words for numbers under 10 and numerals for 10 and greater<\/a>. However, always spell out a number that appears at the start of a sentence (or rephrase).<\/p>\n<p>You should always use numerals for:<\/p>\n<ul>\n<li aria-level=\"1\">Exact numbers before units of measurement or time<\/li>\n<li aria-level=\"1\">Mathematical equations<\/li>\n<li aria-level=\"1\">Percentages and percentiles<\/li>\n<li aria-level=\"1\">Ratios, decimals, and uncommon fractions<\/li>\n<li aria-level=\"1\">Scores and points on scales (e.g., 7-point scale)<\/li>\n<li aria-level=\"1\">Exact amounts of money<\/li>\n<\/ul>\n<h3>Units of measurement and time<\/h3>\n<p>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.<\/p>\n<p>When stating approximate figures, use words to express numbers under 10, and spell out the names of units of measurement.<\/p>\n<figure class=\"kb-textbox border-left green\"><figcaption>Examples: Reporting exact and approximate figures<\/figcaption><ul>\n<li>The ball weighed 7 kg.<\/li>\n<li>The ball weighed approximately seven kilograms.<\/li>\n<\/ul>\n<\/figure>\n<p>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.<\/p>\n<h3>Percentages<\/h3>\n<p>Use numerals for percentages along with the percent symbol (%). Don\u2019t insert a space between the number and the symbol.<\/p>\n<p>Words for \u201cpercent\u201d or \u201cpercentage\u201d should only be used in text when numbers aren\u2019t used, or when a percentage appears at the start of a sentence.<\/p>\n<figure class=\"kb-textbox border-left green\"><figcaption>Examples: Reporting percentages<\/figcaption><ul>\n<li>Of these respondents, 15% agreed with the statement.<\/li>\n<li>Fifteen percent of respondents agreed with the statement.<\/li>\n<li>The percentage was higher in 2020.<\/li>\n<\/ul>\n<\/figure>\n<h2>Decimal places and leading zeros<\/h2>\n<p>The number of decimal places to report depends on what you\u2019re reporting. Generally, you should aim to round numbers while retaining precision. It\u2019s best to present fewer decimal digits to <a href=index-4233.html>aid<\/a> easy understanding.<\/p>\n<p>The following guidelines are usually applicable.<\/p>\n<table class=\"kb-table responsive-inline full-width\">\n<thead>\n<tr>\n<th width=\"50%\">One decimal place<\/th>\n<th>Two decimal places<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\n<ul>\n<li aria-level=\"1\"><a href=index-3020.html>Means<\/a><\/li>\n<li aria-level=\"1\"><a href=index-3024.html>Standard deviations<\/a><\/li>\n<li aria-level=\"1\"><a href=index-2993.html>Descriptive statistics<\/a> based on <a href=index-5004.html#meaning\">discrete<\/a> data<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li aria-level=\"1\"><a href=index-5005.html>Correlation coefficients<\/a><\/li>\n<li aria-level=\"1\">Proportions<\/li>\n<li aria-level=\"1\">Inferential <a href=index-3031.html>test statistics<\/a> such as <em>t <\/em>values, <em>F<\/em> values, and chi-squares<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Use <strong>two or three decimal places<\/strong> and report exact values for all <a href=index-3032.html><em>p<\/em> values<\/a> greater than .001. For <em>p <\/em>values smaller than .001, report them as <em>p<\/em> &lt; .001.<\/p>\n<h3>Leading zeros<\/h3>\n<p>A leading zero is zero before the decimal point for numbers less than one. In APA Style, it\u2019s only used in some cases.<\/p>\n<p>Use a leading zero only when the statistic you\u2019re describing can be greater than one. If it can never exceed one, omit the leading zero.<\/p>\n<table class=\"kb-table responsive-inline full-width\">\n<thead>\n<tr>\n<th width=\"50%\">Use a leading zero<\/th>\n<th>Don\u2019t use a leading zero<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\n<ul>\n<li aria-level=\"1\">Variables that can be greater than 1 (e.g., height or weight)<\/li>\n<li aria-level=\"1\">Cohen\u2019s <em>d<\/em><\/li>\n<li aria-level=\"1\"><em>t<\/em> values<\/li>\n<li aria-level=\"1\"><em>F <\/em>value<\/li>\n<li aria-level=\"1\"><em>z<\/em> values<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li aria-level=\"1\"><em>p<\/em> values<\/li>\n<li aria-level=\"1\"><a href=index-5006.html>Pearson correlation coefficient<\/a><\/li>\n<li aria-level=\"1\">Coefficient of determination<\/li>\n<li aria-level=\"1\">Cronbach\u2019s alpha<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<figure class=\"kb-textbox border-left green\"><figcaption>Examples: Use of decimal places and leading zeros<\/figcaption><ul>\n<li aria-level=\"1\">Consumers reported high satisfaction with the services (<em>M<\/em> = 4.1, <em>SD<\/em> = 0.8).<\/li>\n<li aria-level=\"1\">The correlation was medium-sized (<em>r<\/em> = .35).<\/li>\n<li>Although significant results were obtained, the effect was relatively small (<em>p<\/em> = .015, <em>d<\/em> = 0.11).<\/li>\n<\/ul>\n<\/figure>\n<h2>Formatting mathematical formulas<\/h2>\n<p>Provide formulas only when you use new or uncommon equations. For short equations, present them within one line in the main text whenever possible.<\/p>\n<p>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.<\/p>\n<figure class=\"kb-textbox border-left green\"><figcaption>Example: Short mathematical formula<\/figcaption>We used the formula <em>c<\/em> = [(<em>x<\/em> \u2212 1)\/<em>b<\/em>]<sup>-1<\/sup> in our analysis.<\/figure>\n<p>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.<\/p>\n<figure class=\"kb-textbox border-left green\"><figcaption>Example: Numbering mathematical formulas<\/figcaption><p class=\"ql-left-displayed-equation\" style=\"line-height: 21px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img decoding=\"async\" src=index-5007.html height=\"21\" width=\"573\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;&#92;&#115;&#113;&#114;&#116;&#091;&#51;&#093;&#123;&#120;&#125;&#45;&#51;&#97;&#99;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#40;&#49;&#41;&#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<p class=\"ql-left-displayed-equation\" style=\"line-height: 33px;\"><span class=\"ql-right-eqno\"> &nbsp; <\/span><span class=\"ql-left-eqno\"> &nbsp; <\/span><img decoding=\"async\" src=index-5008.html height=\"33\" width=\"575\" class=\"ql-img-displayed-equation quicklatex-auto-format\" alt=\"&#92;&#98;&#101;&#103;&#105;&#110;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;&#92;&#100;&#102;&#114;&#97;&#99;&#123;&#97;&#99;&#125;&#123;&#120;&#94;&#51;&#125;&#45;&#52;&#99;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#92;&#44;&#40;&#50;&#41;&#92;&#101;&#110;&#100;&#123;&#101;&#113;&#117;&#97;&#116;&#105;&#111;&#110;&#42;&#125;\" title=\"Rendered by QuickLaTeX.com\"\/><\/p>\n<\/figure>\n<h2>Formatting statistical terms<\/h2>\n<p>When reporting statistical <a href=index-3040.html>results<\/a>, present information in easily understandable ways. You can use a mix of text, <a href=index-3486.html>tables, and figures<\/a> to present data effectively when you have a lot of numbers to report.<\/p>\n<p>In your main text, use helpful words like \u201crespectively\u201d or \u201cin order\u201d\u00a0 to aid understanding when listing several statistics in a sequence.<\/p>\n<p>The APA manual provides guidelines for dealing with statistical terms, symbols and abbreviations.<\/p>\n<h3>Symbols and abbreviations<\/h3>\n<p><a href=index-3026.html>Population parameters<\/a> are often represented with Greek letters, while sample statistics are often represented with italicized Latin letters.<\/p>\n<p>Use the population symbol (<em>N<\/em>) for the total number of elements in a sample, and use the sample symbol (<em>n<\/em>) for the number of elements in each subgroup of the full sample.<\/p>\n<p>In general, <a href=index-977.html>abbreviations<\/a> should be defined on first use, but this isn&#8217;t always the case for common statistical abbreviations.<\/p>\n<table class=\"kb-table responsive-inline full-width\">\n<thead>\n<tr>\n<th width=\"50%\">Define<\/th>\n<th width=\"50%\">Don\u2019t define<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\n<ul>\n<li>Abbreviations that do not represent statistics: ANOVA, CI, CFA<\/li>\n<li>Non-standard abbreviations that appear in tables and figures, even if they are already defined in the text.<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li>Statistical symbols or abbreviations: <em style=\"font-family: inherit; font-size: inherit;\">M, <\/em><em>SD, F, t, df, p, N, n, OR<\/em><\/li>\n<li>Greek letters: \u03b1, \u03b2, \u03c7<sup>2<\/sup><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"kb-table responsive-inline full-width\">\n<thead>\n<tr>\n<th width=\"50%\">Use symbols for statistical terms<\/th>\n<th width=\"50%\">Use words for statistical terms<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>When directly referring to a numerical quantity or operator: <em>M<\/em> = 5.41<\/td>\n<td>In the main text: \u201cthe mean accuracy was higher&#8230;\u201d<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>Capitalization, italicization and hyphenation<\/h3>\n<p>Statistical terms such as <em>t<\/em> test, <em>z <\/em>test, and <em>p<\/em> value always begin with a lowercase, italicized letter. Never begin a sentence with lowercase statistical abbreviations.<\/p>\n<p>These statistical terms should only be <a href=index-3485.html>hyphenated<\/a> when they modify a subsequent word (e.g., \u201c<em>z<\/em>-test results\u201d versus results of \u201c<em>z<\/em> tests\u201d).<\/p>\n<p>You can form plurals of statistical symbols (e.g., <em>M<\/em> or <em>p<\/em>) by adding a non-italicized \u201cs\u201d to the end with no apostrophe (e.g., <em>M<\/em>s or <em>p<\/em>s).<\/p>\n<p>In general, the following guidelines apply.<\/p>\n<table class=\"kb-table responsive-inline full-width\">\n<thead>\n<tr>\n<th width=\"50%\">Italicize<\/th>\n<th width=\"50%\">Don\u2019t italicize<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\n<ul>\n<li>Letters when they are statistical symbols or algebraic variables: Cohen\u2019s <em>d<\/em><span>, <\/span><em>SD, p <\/em>value, <em>t<\/em><span> test<\/span><\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li>Greek letters: \u03c3 or \u03a7<sup>2<\/sup><\/li>\n<li>Subscripts for statistical symbols: <em>M<\/em><sub>control<\/sub><\/li>\n<li>Trigonometric terms: sin, cos<\/li>\n<li>Vectors or matrices (boldface these instead): <strong>V, X\u00a0<\/strong><\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table class=\"kb-table responsive-inline full-width\">\n<thead>\n<tr>\n<th width=\"50%\">Capitalize<\/th>\n<th width=\"50%\">Don\u2019t capitalize<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Names of effects or variables only when they appear with multiplication signs: Age \u00d7 Sex effect<\/td>\n<td>Lowercase statistical terms: <em>t<\/em> test, <em>p<\/em> value<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>Parentheses vs. brackets<\/h3>\n<p>Always aim to avoid nested parentheses and brackets when reporting statistics. Instead, you should use commas to separate related statistics.<\/p>\n<table class=\"kb-table responsive-inline full-width\">\n<thead>\n<tr>\n<th width=\"50%\">Use parentheses (round brackets)<\/th>\n<th width=\"50%\">Use (square) brackets<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\n<ul>\n<li><a href=index-4998.html>Degrees of freedom<\/a><\/li>\n<li>Statistical values when they aren\u2019t already in parentheses<\/li>\n<\/ul>\n<\/td>\n<td>\n<ul>\n<li>Confidence interval limits<\/li>\n<li>Statistics in a text that\u2019s already enclosed within parentheses<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<figure class=\"kb-textbox border-left green\"><figcaption>Examples: Reporting values in parentheses<\/figcaption><ul>\n<li>Scores improved between the pretest and posttest (<em>p<\/em> &lt; .001).<\/li>\n<li aria-level=\"1\">Significant differences in test scores were recorded, <em>F<\/em>(1, 30) = 4.67, <em>p<\/em> = .003.<\/li>\n<li aria-level=\"1\">(A previous meta-analysis highlighted low effect sizes [<em>d <\/em>= 0.1] in the field).<\/li>\n<\/ul>\n<\/figure>\n<h2>Reporting means and standard deviations<\/h2>\n<p>Report <a href=index-2993.html>descriptive statistics<\/a> 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.<\/p>\n<p><a href=index-3020.html>Means<\/a> and <a href=index-3024.html>standard deviations<\/a> can be presented in the main text and\/or in parentheses. You don\u2019t need to repeat the units of measurement (e.g., centimeters) for statistics relating to the same data.<\/p>\n<figure class=\"kb-textbox border-left green\"><figcaption>Examples: Reporting mean and standard deviation<\/figcaption><ul>\n<li aria-level=\"1\">Average sample height was 136.4 cm (<em>SD<\/em> = 15.1).<\/li>\n<li aria-level=\"1\">The height of the initial sample was relatively low (<em>M<\/em> = 125.9 cm, <em>SD<\/em> = 16.6).<\/li>\n<li aria-level=\"1\">Height significantly varied between children aged 5\u20137, 8\u201310, and 11\u201313. The means were 115.3, 133.5, and 149.1 cm, respectively.<\/li>\n<\/ul>\n<\/figure>\n<h2>Reporting chi-square tests<\/h2>\n<p>To report the results of a <a href=index-3044.html>chi-square test<\/a>, include the following:<\/p>\n<ul class=\"kb-checklist\">\n<li aria-level=\"1\">the degrees of freedom (<em>df<\/em>) in parentheses<\/li>\n<li>the chi-square (\u03a7<sup>2<\/sup>) value (also referred to as the chi-square test statistic)<\/li>\n<li aria-level=\"1\">the <em>p<\/em> value<\/li>\n<\/ul>\n<figure class=\"kb-textbox border-left green\"><figcaption>Example: Reporting chi-square test results<\/figcaption><ul>\n<li aria-level=\"1\">A <a href=index-5009.html>chi-square test of independence<\/a> revealed a significant association between gender and product preference, \u03a7<sup>2<\/sup>(8) = 19.7, <em>p<\/em> = .012.<\/li>\n<li aria-level=\"1\">Based on a <a href=index-5010.html>chi-square test of goodness of fit<\/a>, \u03a7<sup>2<\/sup>(4) = 11.34, <em>p<\/em> = .023, the sample\u2019s distribution of religious affiliations matched that of the population\u2019s.<\/li>\n<\/ul>\n<\/figure>\n<h2>Reporting <em>z<\/em> tests and <em>t<\/em> tests<\/h2>\n<h3>For <em>z<\/em> tests<\/h3>\n<p>To report the results of a <em>z<\/em> test, include the following:<\/p>\n<ul class=\"kb-checklist\">\n<li aria-level=\"1\">the <em>z <\/em>value (also referred to as the <em>z<\/em> statistic or <em>z<\/em> score)<\/li>\n<li aria-level=\"1\">the <em>p<\/em> value<\/li>\n<\/ul>\n<figure class=\"kb-textbox border-left green\"><figcaption>Example: Reporting z test results<\/figcaption><ul>\n<li aria-level=\"1\">The participants\u2019 scores were higher than the population average, <em>z<\/em> = 2.48, <em>p<\/em> = .013.<\/li>\n<li aria-level=\"1\">Higher scores were obtained on the new 20-item scale compared to the previous 40-item scale, <em>z<\/em> = 2.67, <em>p<\/em> = .007.<\/li>\n<\/ul>\n<\/figure>\n<h3>For <em>t<\/em> tests<\/h3>\n<p>To report the results of a <a href=index-3037.html><em>t<\/em> test<\/a>, include the following:<\/p>\n<ul class=\"kb-checklist\">\n<li>the degrees of freedom (<em>df<\/em>) in parentheses<\/li>\n<li aria-level=\"1\">the <em>t <\/em>value (also referred to as the <em>t<\/em> statistic)<\/li>\n<li aria-level=\"1\">the <em>p<\/em> value<\/li>\n<\/ul>\n<figure class=\"kb-textbox border-left green\"><figcaption>Example: Reporting t test results<\/figcaption><ul>\n<li aria-level=\"1\">Older adults experienced significantly more loneliness than younger adults, <em>t<\/em>(32) = 2.94, <em>p<\/em> = .006.<\/li>\n<li aria-level=\"1\">Reaction times were significantly faster for mice in the experimental condition, <em>t<\/em>(53) = 5.94, <em>p<\/em> &lt; .001.<\/li>\n<\/ul>\n<\/figure>\n<h2>Reporting analysis of variance (ANOVAs)<\/h2>\n<p>To report the results of an <a href=index-3038.html>ANOVA<\/a>, include the following:<\/p>\n<ul class=\"kb-checklist\">\n<li aria-level=\"1\">the degrees of freedom (between groups, within groups) in parentheses<\/li>\n<li>the <em>F <\/em>value (also referred to as the <em>F <\/em>statistic)<\/li>\n<li aria-level=\"1\">the <em>p<\/em> value<\/li>\n<\/ul>\n<figure class=\"kb-textbox border-left green\"><figcaption>Example: Reporting ANOVA results<\/figcaption><ul>\n<li aria-level=\"1\">A one-way ANOVA demonstrated that the effect of leadership style was significant for employee engagement, <em>F<\/em>(2, 78) = 4.58, <em>p<\/em> = .013.<\/li>\n<li aria-level=\"1\">We found a statistically significant main effect of age group on social media use, <em>F<\/em>(3, 117) = 3.19, <em>p<\/em> = .026.<\/li>\n<\/ul>\n<\/figure>\n<h2>Reporting correlations<\/h2>\n<p>To report the results of a correlation, include the following:<\/p>\n<ul class=\"kb-checklist\">\n<li aria-level=\"1\">the degrees of freedom in parentheses<\/li>\n<li aria-level=\"1\">the <em>r <\/em>value (the correlation coefficient)<\/li>\n<li aria-level=\"1\">the <em>p<\/em> value<\/li>\n<\/ul>\n<figure class=\"kb-textbox border-left green\"><figcaption>Example: Reporting correlation results<\/figcaption><ul>\n<li aria-level=\"1\">We found a strong correlation between average temperature and new daily cases of COVID-19, <em>r<\/em> (357)\u00a0= .42, <em>p<\/em> &lt; .001.<\/li>\n<\/ul>\n<\/figure>\n<h2>Reporting regressions<\/h2>\n<p>Results of <a href=index-3035.html>regression analyses<\/a> are often displayed in a table because the output includes many numbers.<\/p>\n<p>To report the results of a regression analysis in the text, include the following:<\/p>\n<ul class=\"kb-checklist\">\n<li aria-level=\"1\">the <em>R<\/em><sup>2 <\/sup>value (the coefficient of determination)<\/li>\n<li aria-level=\"1\">the <em>F<\/em> value (also referred to as the <em>F <\/em>statistic)<\/li>\n<li aria-level=\"1\">the <a href=index-4998.html>degrees of freedom<\/a> in parentheses<\/li>\n<li aria-level=\"1\">the <em>p<\/em> value<\/li>\n<\/ul>\n<p>The format is usually:<\/p>\n<figure class=\"kb-textbox border-left green\"><figcaption>Example: Reporting regression results<\/figcaption><ul>\n<li aria-level=\"1\">SAT scores predicted college GPA, <em>R<\/em><sup>2<\/sup> = .34, <em>F<\/em>(1, 416) = 6.71, <em>p<\/em> = .009.<\/li>\n<\/ul>\n<\/figure>\n<h2>Reporting confidence intervals<\/h2>\n<p>You should report<a href=index-3028.html> confidence intervals<\/a> of effect sizes (e.g., Cohen\u2019s <em>d<\/em>) or point estimates where relevant.<\/p>\n<p>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.<\/p>\n<figure class=\"kb-textbox border-left green\"><figcaption>Example: Reporting confidence intervals<\/figcaption><ul>\n<li aria-level=\"1\">Older adults experienced significantly more loneliness than younger adults, <em>t<\/em>(32) = 2.94, <em>p<\/em> = .006, <em>d<\/em> = 0.81, 95% CI [0.6, 1.02].<\/li>\n<li aria-level=\"1\">On average, the treatment resulted in a 30% reduction in migraine frequency, 99% CI [26.5, 33.5].<\/li>\n<\/ul>\n<\/figure>\n<p>When presenting multiple confidence intervals with the same confidence levels in a sequence, don\u2019t repeat the confidence level or the word \u201cCI.\u201d<\/p>\n<h2 id=\"other\">Other interesting articles<\/h2>\n<p data-pm-slice=\"1 1 []\">If you want to know more about <a href=index-2947.html class=\"ProsemirrorEditor-link\">statistics<\/a>, <a href=_-12.html class=\"ProsemirrorEditor-link\">methodology<\/a>, or <a href=index-3462.html class=\"ProsemirrorEditor-link\">research bias<\/a>, make sure to check out some of our other articles with explanations and examples.<\/p>\n<div class=\"container\">\n<div class=\"row\">\n<div class=\"col-md\" style=\"background-color: #e8f2fc; padding: 1.27rem 1.56rem; line-height: 1.8; border-radius: .5rem; margin-right: 0.5rem; margin-top: 0.5rem;\">\n<p><strong><em class=\"fa fa-bar-chart\" aria-hidden=\"true\"><\/em>Statistics<\/strong><\/p>\n<ul style=\"padding: 5px;\">\n<li><a href=index-5009.html>Chi square test of independence<\/a><\/li>\n<li><a href=index-2955.html>Statistical power<\/a><\/li>\n<li><a href=index-2993.html>Descriptive statistics<\/a><\/li>\n<li><a href=index-4998.html>Degrees of freedom<\/a><\/li>\n<li><a href=index-5006.html>Pearson correlation<\/a><\/li>\n<li><a href=index-2954.html>Null hypothesis<\/a><\/li>\n<\/ul>\n<\/div>\n<div class=\"col-md\" style=\"background-color: #e8f2fc; padding: 1.27rem 1.56rem; line-height: 1.8; border-radius: .5rem; margin-right: 0.5rem; margin-top: 0.5rem;\">\n<p><strong><em class=\"fa fa-list-ul\" aria-hidden=\"true\"><\/em> Methodology<\/strong><\/p>\n<ul style=\"padding: 5px;\">\n<li><a href=index-4137.html>Double-blind study<\/a><\/li>\n<li><a href=index-5011.html>Case-control study<\/a><\/li>\n<li><a href=index-4154.html>Research ethics<\/a><\/li>\n<li><a href=index-2779.html>Data collection<\/a><\/li>\n<li><a href=index-4141.html>Hypothesis testing<\/a><\/li>\n<li><a href=index-4145.html>Structured interviews<\/a><\/li>\n<\/ul>\n<\/div>\n<div class=\"col-md\" style=\"background-color: #e8f2fc; padding: 1.27rem 1.56rem; line-height: 1.8; border-radius: .5rem; margin-right: 0.5rem; margin-top: 0.5rem;\">\n<p><strong><em class=\"fa fa-globe\" aria-hidden=\"true\"><\/em> Research bias<\/strong><\/p>\n<ul style=\"padding: 5px;\">\n<li><a href=index-2963.html>Hawthorne effect<\/a><\/li>\n<li><a href=index-3983.html>Unconscious bias<\/a><\/li>\n<li><a href=index-4339.html>Recall bias<\/a><\/li>\n<li><a href=index-3278.html>Halo effect<\/a><\/li>\n<li><a href=index-3276.html>Self-serving bias<\/a><\/li>\n<li><a href=index-4129.html>Information bias<\/a><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n    <h2>Frequently asked questions about APA Style statistics<\/h2>\n<dl class=\"faq-list faq-list--arrows w-100 my-5\" itemscope itemtype=\"https:\/\/schema.org\/FAQPage\">\n            <div itemscope itemprop=\"mainEntity\" itemtype=\"https:\/\/schema.org\/Question\">\n            <dt id=\"statistical-results-to-report-apa-style\" class=\"faq-list__title\">\n                <a href=index-5000.html class=\"faq-list__link qa-faq-anchor\">\n                    <span itemprop=\"name\">\n                        What statistical results do you need to report according to APA style?\n                    <\/span>\n                <\/a>\n            <\/dt>\n            <dd id=\"statistical-results-to-report-apa-style-answer\" class=\"faq-list__answer qa-faq-answer kb-article-styles\" itemscope itemprop=\"acceptedAnswer\" itemtype=\"https:\/\/schema.org\/Answer\">\n                <div itemprop=\"text\">\n                                        <p>According to the APA guidelines, you should report enough detail on<a href=index-2994.html> inferential statistics<\/a> so that your readers understand your analyses.<\/p>\n<p>Report the following for each hypothesis test:<\/p>\n<ul>\n<li>the <a href=index-3031.html>test statistic<\/a> value<\/li>\n<li>the <a href=index-4998.html>degrees of freedom<\/a><\/li>\n<li>the exact <a href=index-3032.html><em>p<\/em> value<\/a> (unless it is less than 0.001)<\/li>\n<li>the magnitude and direction of the effect<\/li>\n<\/ul>\n<p>You should also present <a href=index-3028.html>confidence intervals<\/a> and estimates of <a href=index-2957.html>effect sizes<\/a> where relevant.<\/p>\n\n                <\/div>\n            <\/dd>\n        <\/div>\n            <div itemscope itemprop=\"mainEntity\" itemtype=\"https:\/\/schema.org\/Question\">\n            <dt id=\"how-many-decimal-places-apa-style\" class=\"faq-list__title\">\n                <a href=index-5012.html class=\"faq-list__link qa-faq-anchor\">\n                    <span itemprop=\"name\">\n                        How many decimal places do you use in APA style?\n                    <\/span>\n                <\/a>\n            <\/dt>\n            <dd id=\"how-many-decimal-places-apa-style-answer\" class=\"faq-list__answer qa-faq-answer kb-article-styles\" itemscope itemprop=\"acceptedAnswer\" itemtype=\"https:\/\/schema.org\/Answer\">\n                <div itemprop=\"text\">\n                                        <p>The number of decimal places to report depends on what you\u2019re reporting. Generally, you should aim to round numbers while retaining precision. It\u2019s best to present fewer decimal digits to <a href=index-4233.html>aid<\/a> easy understanding.<\/p>\n<p>Use one decimal place for:<\/p>\n<ul>\n<li><a href=index-3020.html>Means<\/a><\/li>\n<li><a href=index-3024.html>Standard deviations<\/a><\/li>\n<li><a href=index-2993.html>Descriptive statistics<\/a> based on <a href=index-5013.html>discrete data<\/a><\/li>\n<\/ul>\n<p>Use two decimal places for:<\/p>\n<ul>\n<li>Correlation coefficients<\/li>\n<li>Proportions<\/li>\n<li>Inferential<a href=index-3031.html> test statistics<\/a> such as <em>t<\/em> values, <em>F<\/em> values, and chi-squares.<\/li>\n<\/ul>\n\n                <\/div>\n            <\/dd>\n        <\/div>\n            <div itemscope itemprop=\"mainEntity\" itemtype=\"https:\/\/schema.org\/Question\">\n            <dt id=\"when-to-use-tables-or-figures-in-apa\" class=\"faq-list__title\">\n                <a href=index-5001.html class=\"faq-list__link qa-faq-anchor\">\n                    <span itemprop=\"name\">\n                        When should I use tables or figures to present numbers?\n                    <\/span>\n                <\/a>\n            <\/dt>\n            <dd id=\"when-to-use-tables-or-figures-in-apa-answer\" class=\"faq-list__answer qa-faq-answer kb-article-styles\" itemscope itemprop=\"acceptedAnswer\" itemtype=\"https:\/\/schema.org\/Answer\">\n                <div itemprop=\"text\">\n                                        <p>In APA style, statistics can be presented in the main text or as <a href=index-3486.html>tables or figures<\/a>. To decide how to present numbers, you can follow APA guidelines:<\/p>\n<ul>\n<li>To present three or fewer numbers, try a sentence,<\/li>\n<li>To present between 4 and 20 numbers, try a table,<\/li>\n<li>To present more than 20 numbers, try a figure.<\/li>\n<\/ul>\n<p>Since these are general guidelines, use your own judgment and feedback from others for effective presentation of numbers.<\/p>\n\n                <\/div>\n            <\/dd>\n        <\/div>\n    <\/dl>\n","protected":false},"excerpt":{"rendered":"<p>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 [&hellip;]<\/p>\n","protected":false},"author":115,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_relevanssi_hide_post":"","_relevanssi_hide_content":"","_relevanssi_pin_for_all":"","_relevanssi_pin_keywords":"","_relevanssi_unpin_keywords":"","_relevanssi_related_keywords":"","_relevanssi_related_include_ids":"","_relevanssi_related_exclude_ids":"","_relevanssi_related_no_append":"","_relevanssi_related_not_related":"","_relevanssi_related_posts":"","_relevanssi_noindex_reason":""},"categories":[85],"tags":[],"acf":[],"yoast_head":"<title>Reporting Statistics in APA Style | Guidelines &amp; Examples<\/title>\n
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