{"id":1035,"date":"2026-10-14T07:16:00","date_gmt":"2026-10-14T07:16:00","guid":{"rendered":"https:\/\/freestatisticaltools.com\/blog\/?p=1035"},"modified":"2026-10-14T07:16:00","modified_gmt":"2026-10-14T07:16:00","slug":"which-statistical-test-to-use","status":"publish","type":"post","link":"https:\/\/freestatisticaltools.com\/blog\/which-statistical-test-to-use\/","title":{"rendered":"Which Statistical Test Should I Use? A Simple Decision Guide"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Choosing a statistical test feels hard because there are dozens of them. In practice, almost every choice comes down to <strong>three questions<\/strong>: what you want to find out, what kind of variables you have, and how your data were collected. Answer those, and the list shrinks to one or two candidates.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This guide walks through the three questions, gives you a quick lookup table, and links each test to a free tool on FreeStatisticalTools.com that runs in your browser.<\/p>\n\n\n\n<div class=\"fst-takeaways\"><b>Key takeaways<\/b><ul><li><strong>Goal:<\/strong> are you comparing groups, looking for a relationship, predicting an outcome, or checking a measure?<\/li><li><strong>Variables:<\/strong> is your outcome continuous (numbers), ordinal (ranks) or categorical (groups)?<\/li><li><strong>Design:<\/strong> are the groups independent (different people) or related (the same people measured twice)?<\/li><li>Check assumptions before you trust a parametric test, and have a nonparametric backup ready.<\/li><\/ul><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Question 1: What do you want to find out?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Most research questions fall into one of five families:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Compare groups.<\/strong> &quot;Do men and women differ in stress scores?&quot; &quot;Did scores change after training?&quot; These call for t-tests, ANOVA or their nonparametric versions.<\/li>\n\n<li><strong>Look for a relationship.<\/strong> &quot;Is study time related to exam marks?&quot; This is a correlation question.<\/li>\n\n<li><strong>Predict an outcome.<\/strong> &quot;Which factors predict purchase intention?&quot; This is regression.<\/li>\n\n<li><strong>Test an association between categories.<\/strong> &quot;Is smoking status related to gender?&quot; This is a chi-square-type question.<\/li>\n\n<li><strong>Check a measurement.<\/strong> &quot;Is my questionnaire reliable?&quot; &quot;Do my items measure the constructs I think they measure?&quot; This is reliability analysis or factor analysis.<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">If your question involves <em>why<\/em> or <em>when<\/em> an effect happens (an indirect path through a third variable, or an effect that depends on another variable), you are in mediation and moderation territory, covered at the end of this guide.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Question 2: What type are your variables?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The <strong>outcome<\/strong> (dependent variable) matters most. Statisticians usually group variables into three types:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Type<\/th><th>What it looks like<\/th><th>Examples<\/th><\/tr><\/thead><tbody><tr><td>Continuous (interval\/ratio)<\/td><td>Numbers where differences are meaningful<\/td><td>Age, income, reaction time, a scale score averaged over items<\/td><\/tr><tr><td>Ordinal<\/td><td>Ordered categories, uneven gaps<\/td><td>Single Likert item (1\u20135), education level, rankings<\/td><\/tr><tr><td>Categorical (nominal)<\/td><td>Labels with no order<\/td><td>Gender, country, treatment group, yes\/no<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">A scale score made by averaging several Likert items is normally treated as continuous. A <em>single<\/em> Likert item is safer to treat as ordinal, which points you to nonparametric tests.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Question 3: How was the data collected?<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Independent groups:<\/strong> each person appears in only one group (for example, a treatment group and a control group).<\/li>\n\n<li><strong>Related (paired or repeated) measures:<\/strong> the same people are measured more than once (before and after), or people are matched in pairs.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Using an independent-groups test on paired data (or the reverse) is one of the most common mistakes in student theses, so be clear about this before you choose.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">The quick lookup table<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Find your goal and data type, then follow the link to run the test.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Goal<\/th><th>Outcome<\/th><th>Groups \/ predictors<\/th><th>Parametric test<\/th><th>Nonparametric alternative<\/th><\/tr><\/thead><tbody><tr><td>Compare a mean to a known value<\/td><td>Continuous<\/td><td>One sample<\/td><td><a href=\"\/one-sample-t-test-calculator\/\">One-sample t-test<\/a><\/td><td><a href=\"\/wilcoxon-signed-rank-test-calculator\/\">Wilcoxon signed-rank test<\/a><\/td><\/tr><tr><td>Compare 2 independent groups<\/td><td>Continuous<\/td><td>2 groups<\/td><td><a href=\"\/independent-t-test-calculator\/\">Independent samples t-test<\/a><\/td><td><a href=\"\/mann-whitney-u-test-calculator\/\">Mann-Whitney U test<\/a><\/td><\/tr><tr><td>Compare 2 related measurements<\/td><td>Continuous<\/td><td>Same people twice<\/td><td><a href=\"\/paired-t-test-calculator\/\">Paired t-test<\/a><\/td><td><a href=\"\/wilcoxon-signed-rank-test-calculator\/\">Wilcoxon signed-rank test<\/a><\/td><\/tr><tr><td>Compare 3+ independent groups<\/td><td>Continuous<\/td><td>3+ groups<\/td><td><a href=\"\/one-way-anova-calculator\/\">One-way ANOVA<\/a><\/td><td><a href=\"\/kruskal-wallis-test-calculator\/\">Kruskal-Wallis test<\/a><\/td><\/tr><tr><td>Compare 3+ related measurements<\/td><td>Continuous<\/td><td>Same people 3+ times<\/td><td><a href=\"\/repeated-measures-anova-calculator\/\">Repeated measures ANOVA<\/a><\/td><td><a href=\"\/friedman-test-calculator\/\">Friedman test<\/a><\/td><\/tr><tr><td>Two grouping factors<\/td><td>Continuous<\/td><td>2 factors<\/td><td><a href=\"\/two-way-anova-calculator\/\">Two-way ANOVA<\/a><\/td><td>\u2014<\/td><\/tr><tr><td>Relationship between two variables<\/td><td>Continuous \/ ordinal<\/td><td>\u2014<\/td><td><a href=\"\/correlation-calculator\/\">Pearson correlation<\/a><\/td><td>Spearman correlation (same tool)<\/td><\/tr><tr><td>Predict a continuous outcome<\/td><td>Continuous<\/td><td>1+ predictors<\/td><td><a href=\"\/multiple-regression-calculator\/\">Multiple regression<\/a><\/td><td><a href=\"\/robust-standard-errors-regression-diagnostics\/\">Regression with robust SEs<\/a><\/td><\/tr><tr><td>Predict a yes\/no outcome<\/td><td>Binary<\/td><td>1+ predictors<\/td><td><a href=\"\/logistic-regression-calculator\/\">Logistic regression<\/a><\/td><td>\u2014<\/td><\/tr><tr><td>Association between two categorical variables<\/td><td>Categorical<\/td><td>\u2014<\/td><td><a href=\"\/chi-square-test-calculator\/\">Chi-square test<\/a><\/td><td><a href=\"\/fishers-exact-test-calculator\/\">Fisher&#39;s exact test<\/a> (small samples)<\/td><\/tr><tr><td>Change in a yes\/no outcome, same people<\/td><td>Binary<\/td><td>Paired<\/td><td><a href=\"\/mcnemar-test-calculator\/\">McNemar test<\/a><\/td><td>\u2014<\/td><\/tr><tr><td>Questionnaire reliability<\/td><td>Items<\/td><td>\u2014<\/td><td><a href=\"\/cronbachs-alpha-calculator\/\">Cronbach&#39;s alpha<\/a><\/td><td><a href=\"\/mcdonalds-omega-calculator\/\">McDonald&#39;s omega<\/a><\/td><\/tr><tr><td>Find the structure behind items<\/td><td>Items<\/td><td>\u2014<\/td><td><a href=\"\/exploratory-factor-analysis\/\">Exploratory factor analysis<\/a><\/td><td>\u2014<\/td><\/tr><tr><td>Test a theoretical model with latent variables<\/td><td>Items<\/td><td>Constructs and paths<\/td><td><a href=\"\/cb-sem\/app\/\">CB-SEM Studio<\/a><\/td><td><a href=\"\/pls-sem\/app\/\">PLS-SEM Studio<\/a><\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<div class=\"fst-note tip\"><b>Not sure? Start with descriptive statistics<\/b><p>Before any test, run descriptive statistics and look at a histogram or box plot of each variable. Skewed distributions, outliers or tiny groups will change which test you should use. The <a href=\"\/descriptive-statistics-calculator\/\">descriptive statistics calculator<\/a> gives you means, medians, SDs, skewness and charts in one go.<\/p><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Parametric or nonparametric?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Parametric tests (t-tests, ANOVA, Pearson correlation, regression) compare means and assume, roughly, that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>observations are independent;<\/li>\n\n<li>the outcome (or the model&#39;s residuals) is approximately normally distributed;<\/li>\n\n<li>groups have similar variances (for t-tests and ANOVA).<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">With moderate samples (say, 30 or more per group) these tests are fairly robust to non-normality, thanks to the central limit theorem. They are less forgiving of heavy outliers and very unequal variances. Two practical rules:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Unequal variances?<\/strong> Report Welch&#39;s version. The <a href=\"\/independent-t-test-calculator\/\">independent t-test tool<\/a> shows Student and Welch results side by side, and the <a href=\"\/one-way-anova-calculator\/\">one-way ANOVA tool<\/a> reports Welch&#39;s F.<\/li>\n\n<li><strong>Small, skewed samples or ordinal outcomes?<\/strong> Use the nonparametric alternative from the table above. You can check normality with the <a href=\"\/shapiro-wilk-test-calculator\/\">Shapiro-Wilk test<\/a>, but always look at a plot too: with large samples, the test flags trivial deviations.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Worked examples<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 1.<\/strong> A nurse researcher compares anxiety scores (a 20-item scale) between patients who received a pre-surgery briefing and patients who did not. Outcome: continuous. Groups: two, independent. \u2192 <strong>Independent samples t-test<\/strong> (Welch version if variances differ).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 2.<\/strong> A teacher measures the same 25 students&#39; reading scores in September, January and June. Outcome: continuous. Design: same people, three time points. \u2192 <strong>Repeated measures ANOVA<\/strong>, or the <strong>Friedman test<\/strong> if the scores are badly skewed.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 3.<\/strong> A marketer asks 400 customers whether they would recommend the brand (yes\/no) and records their age group. Two categorical variables. \u2192 <strong>Chi-square test of independence<\/strong>, reporting Cram\u00e9r&#39;s V as the effect size.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example 4.<\/strong> A PhD student surveys 350 employees and wants to know whether job autonomy predicts engagement <em>through<\/em> intrinsic motivation. That is an indirect effect. \u2192 <strong>Mediation analysis<\/strong> with bootstrapped confidence intervals, or a full structural equation model if the constructs are measured with several items each.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Beyond the basics: mediation, moderation and SEM<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Mediation<\/strong> asks whether X affects Y <em>through<\/em> M. Use the <a href=\"\/mediation-analysis-calculator\/\">mediation analysis calculator<\/a> and read our <a href=\"\/blog\/mediation-analysis-bootstrapping\/\">step-by-step mediation guide<\/a>.<\/li>\n\n<li><strong>Moderation<\/strong> asks whether the effect of X on Y <em>depends on<\/em> W. Use the <a href=\"\/moderation-analysis-calculator\/\">moderation analysis calculator<\/a>, which gives simple slopes and the Johnson-Neyman region; see our <a href=\"\/blog\/moderation-analysis-simple-slopes\/\">moderation guide<\/a>.<\/li>\n\n<li><strong>Both together<\/strong> (moderated mediation) are covered by the <a href=\"\/process-macro-online\/\">PROCESS macro online<\/a> tool.<\/li>\n\n<li><strong>Latent variables<\/strong> measured by several questionnaire items are best handled with structural equation modeling. Our comparison of <a href=\"\/blog\/cb-sem-vs-pls-sem\/\">CB-SEM vs PLS-SEM<\/a> helps you choose between the two approaches.<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">Common mistakes to avoid<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Running many t-tests instead of one ANOVA. Each extra test inflates the chance of a false positive.<\/li>\n\n<li>Treating paired data as independent, which throws away power and gives wrong p-values.<\/li>\n\n<li>Using a chi-square test when more than 20% of expected counts are below 5. Switch to Fisher&#39;s exact test for 2\u00d72 tables.<\/li>\n\n<li>Reporting only p-values. Always add an effect size (Cohen&#39;s d, eta squared, r, Cram\u00e9r&#39;s V or an odds ratio) and a confidence interval.<\/li>\n\n<li>Choosing the test after seeing which one gives p &lt; .05. Decide on the analysis before you look at the results.<\/li>\n<\/ul>\n\n\n<aside class=\"fst-cta\"><span class=\"eyebrow\">Free \u00b7 No sign-up \u00b7 Private<\/span><h3>Still not sure which test fits your data?<\/h3><p>The tools home page has a Which test? table that maps each research goal and data type to a free calculator with example data.<\/p><a class=\"btn\" href=\"https:\/\/freestatisticaltools.com\/#which-test\">Open the Which test? table \u2192<\/a><\/aside>\n\n\n\n<h2 class=\"wp-block-heading\">Frequently asked questions<\/h2>\n\n\n\n<div class=\"fst-faq\"><details><summary>How do I know which statistical test to use?<\/summary><div class=\"a\"><p>Answer three questions: what is your goal (compare groups, find a relationship, predict, or check a measure), what type is your outcome variable (continuous, ordinal or categorical), and are your groups independent or related? The lookup table in this guide maps each combination to a test.<\/p><\/div><\/details><details><summary>Should I use a t-test or ANOVA?<\/summary><div class=\"a\"><p>Use a t-test to compare exactly two group means and a one-way ANOVA for three or more groups. With two groups, ANOVA and the t-test give the same p-value (F equals t squared).<\/p><\/div><\/details><details><summary>When should I use a nonparametric test?<\/summary><div class=\"a\"><p>Use one when your outcome is ordinal (for example a single Likert item), when samples are small and clearly skewed, or when there are extreme outliers you cannot justify removing. Nonparametric tests compare ranks rather than means.<\/p><\/div><\/details><details><summary>Can I treat Likert scale data as continuous?<\/summary><div class=\"a\"><p>A scale score that averages several Likert items is usually treated as continuous and analysed with parametric tests. A single Likert item is better treated as ordinal, so use tests such as the Mann-Whitney U or Kruskal-Wallis test.<\/p><\/div><\/details><details><summary>Is there free software that runs these tests?<\/summary><div class=\"a\"><p>Yes. Every test linked in this guide runs free in your browser on FreeStatisticalTools.com, with no sign-up, and your data stays on your device. Results come out as APA-style tables.<\/p><\/div><\/details><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Answer three questions about your goal, your variables and your design, and this guide points you to the right test, with a free tool to run it.<\/p>\n","protected":false},"author":1,"featured_media":1036,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_fst_seo_title":"Which Statistical Test to Use? Decision Guide with Free Tools","_fst_meta_desc":"Pick the right statistical test in three questions: your goal, your variable types and your design. 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