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Statistical Methods
The procedures psychology research actually uses, organized by what they do.
The list follows Blanca, Alarcón and Bono (2018), a review of the analyses published in psychology journals. We split some of the paper's combined categories into separate procedures so each gets its own page.
72 methods
Descriptive and Distribution
Summarizing data and describing its shape.
- Descriptive Statistics Descriptive statistics summarize your data's typical value, spread and shape. Descriptive statistics summarize what your data look like. For numeric scores, they describe the typical value, the spread and the shape of the distribution.
- Distribution Fitting Distribution fitting checks whether scores follow a named shape, like the normal. Distribution fitting estimates a named distribution, most often the normal curve, from one variable's scores and checks how well it describes them, usually with a goodness-of-fit test of whether the scores could have come from it.
Agreement and Reliability
How consistently raters, items or occasions measure the same thing.
- Cohen's Kappa Cohen's kappa measures how much two raters agree beyond chance. Cohen's kappa takes two raters' category codes for the same cases and measures how much they agree beyond the agreement chance alone would produce.
- Weighted Kappa Weighted kappa measures two raters' agreement on an ordered scale. Weighted kappa takes two raters' ratings of the same cases on an ordered scale and measures how much they agree beyond chance, giving partial credit when their ratings are close.
- Fleiss' Kappa Fleiss' kappa measures how much three or more raters agree beyond chance. Fleiss' kappa takes category codes from three or more raters for the same cases and measures how much they agree beyond the agreement chance alone would produce.
- Intraclass Correlation Coefficient (ICC) The ICC measures how consistently raters score the same targets. The intraclass correlation coefficient takes continuous scores that several raters (or occasions) gave the same targets and estimates how much of their variation reflects real differences between targets.
- Cronbach's Alpha Cronbach's alpha measures how well a scale's items hang together. Cronbach's alpha shows how strongly a set of items meant to measure one thing hang together and, under certain assumptions, estimates how reliable their total score is.
- McDonald's Omega McDonald's omega estimates how reliable a scale's total score is. McDonald's omega takes a set of items that measure one trait and estimates how much of the variation in their total score reflects the factor they share.
- Test-Retest Reliability Test-retest reliability checks whether a measure gives people the same scores twice. Test-retest reliability takes the same measure given twice to the same people and estimates how closely their two scores agree, which shows how much of the variation between people's scores reflects stable differences rather than occasion effects and measurement error.
- Krippendorff's Alpha Krippendorff's alpha measures coders' agreement beyond chance, even with missing codes. Krippendorff's alpha takes codes from any number of coders, with some codes missing, and measures how much they agree beyond chance on a nominal, ordinal, interval or ratio scale.
Correlation and Association
Whether, and how strongly, two variables move together.
- Pearson Correlation Pearson's correlation measures the strength and direction of a straight-line relationship. Pearson correlation takes two continuous variables measured on the same people and tests whether they share a straight-line relationship: which way it runs and how strong it is.
- Spearman Correlation Spearman's correlation measures how consistently two ordered variables rise or fall together. Spearman correlation takes two variables measured on the same people, ranks each one, and tests whether higher ranks on one go with higher (or lower) ranks on the other.
- Comparing Correlation Coefficients Comparing correlation coefficients tests whether the strength or direction of a relationship differs between two independent groups. Comparing correlation coefficients takes the same two variables measured in two independent groups and tests whether their correlations differ in strength or direction.
- Partial Correlation Partial correlation measures how two variables are related after statistically accounting for other variables. Partial correlation takes two continuous variables and a third measured on the same people, and tests how strongly the two are related once the third's straight-line part is removed from both.
- Goodman and Kruskal's Gamma Gamma measures whether two ordered variables rise and fall together. Goodman and Kruskal's gamma takes two ordered categorical variables measured on the same people and tests whether higher categories on one tend to go with higher categories on the other.
- Cramér's V Cramér's V measures how strongly two categorical variables are related. Cramér's V takes two categorical variables measured on the same people and measures how strongly they're associated, on a 0-to-1 scale that, unlike χ², is standardized for sample size.
- Somers' D Somers' d measures how well one ordered variable predicts another's order. Somers' d takes two ordered variables measured on the same people, one treated as the predictor, and measures how well the predictor's order foretells the outcome's order, with a z test of whether it differs from zero.
- Contingency Coefficient The contingency coefficient measures how strongly two categorical variables are related. The contingency coefficient takes two categorical variables measured on the same people and measures how strongly they're associated, by rescaling the chi-square statistic onto a scale that never quite reaches 1.
Categorical Data and Proportions
Counts and proportions across categories.
- Pearson Chi-Square Test A chi-square test checks whether two categorical variables are related. A Pearson chi-square test asks whether the categories of two variables go together more than we'd expect by chance. It compares how many people actually fall into each combination with how many we'd expect if the variables were unrelated.
- Fisher's Exact Test Fisher's exact test checks whether two yes/no variables are related. Fisher's exact test takes a two-by-two table of counts, such as a yes/no outcome in two groups, and tests whether the variables are related, with exact probabilities that hold in small samples.
- McNemar's Test McNemar's test checks whether a yes/no proportion changed in the same people. McNemar's test takes a yes/no outcome measured twice in the same people and tests whether the proportion answering yes changed between the two measurements.
- Cochran's Q Cochran's Q compares yes/no proportions in the same people across conditions. Cochran's Q takes a yes/no outcome measured in the same people under three or more conditions or at three or more times and tests whether the proportion answering yes is the same in all of them.
- z-Test for Proportions A z-test for proportions compares a yes/no proportion between two groups. A z-test for proportions takes a yes/no outcome measured in two separate groups of people and tests whether the share answering yes differs between the two populations.
- Binomial Test The binomial test checks a yes/no proportion against a set value. The exact binomial test takes a yes/no outcome from one group and tests whether the share answering yes differs from a fixed value, using exact probabilities that hold in small samples.
Nonparametric Group Comparisons
Comparing groups using ranks instead of raw scores.
- Mann-Whitney U Test The Mann-Whitney U test compares ranked scores between two separate groups. The Mann-Whitney U test takes ranked or skewed scores from two separate groups and tests whether scores in one group tend to be higher than in the other.
- Wilcoxon Signed-Rank Test The Wilcoxon signed-rank test compares two ranked measurements from the same people. A Wilcoxon signed-rank test takes an ordinal or skewed outcome measured twice in the same people and tests whether their changes lean up or down more than chance would allow.
- Kruskal-Wallis Test The Kruskal-Wallis test compares ranked scores across three or more separate groups. A Kruskal-Wallis test takes an ordinal or skewed outcome from three or more separate groups, ranks everyone together, and tests whether some groups tend to score higher than others.
- Friedman Test The Friedman test compares ranked scores from the same people across conditions. The Friedman test takes an ordinal or skewed outcome measured in the same people under three or more conditions and tests whether people tend to score higher in some conditions than in others.
t-Tests
Comparing one or two means.
- One-Sample t-Test A one-sample t-test compares a sample's mean with a set value. A one-sample t-test takes one continuous variable from one sample and tests whether its population mean differs from a specified value.
- Independent-Samples t-Test An independent-samples t-test compares the means of two separate groups. An independent-samples t-test takes one continuous outcome measured in two separate groups of people and tests whether the two population means differ.
- Paired-Samples t-Test A paired-samples t-test compares two measurements from the same people. A paired-samples t-test takes one continuous outcome measured twice in the same people and tests whether the average change between the two measurements differs from zero.
- Bayesian Independent-Samples t-Test A Bayesian t-test weighs the evidence for and against two groups differing. A Bayesian independent-samples t-test takes one continuous outcome from two separate groups and weighs how much the data favor a difference between the population means over none, or the reverse.
ANOVA Family
Comparing means across three or more groups or conditions.
- One-Way Between-Subjects ANOVA A one-way ANOVA compares the means of three or more separate groups. A one-way between-subjects ANOVA takes one continuous outcome from three or more separate groups and tests whether their population means all equal each other.
- One-Way Repeated-Measures ANOVA A repeated-measures ANOVA compares the same people's means across three-plus conditions. A one-way repeated-measures ANOVA takes one continuous outcome measured in the same people under three or more conditions and tests whether the condition means all equal each other.
- Factorial Between-Subjects ANOVA A factorial ANOVA tests several factors' effects and whether they interact. A factorial between-subjects ANOVA takes one continuous outcome from separate groups formed by crossing two or more factors and tests each factor's effect and whether the factors' effects depend on each other.
- Factorial Repeated-Measures ANOVA A factorial repeated-measures ANOVA tests two within-person factors and their interaction. A factorial repeated-measures ANOVA takes one continuous outcome, measured in the same people under every combination of two within-person factors, and tests each factor's main effect and their interaction.
- Mixed Factorial ANOVA A mixed ANOVA tests whether separate groups change differently across repeated measurements. A mixed factorial ANOVA takes one continuous outcome, measured repeatedly in two or more separate groups, and tests whether the groups differ, whether scores change, and whether the groups change differently.
- Bayesian ANOVA A Bayesian ANOVA weighs the evidence for and against group means differing. A Bayesian ANOVA takes one continuous outcome from three or more separate groups and weighs how much the data favor different population means over equal ones, or the reverse.
- ANCOVA ANCOVA compares group means after adjusting for another variable, like a pretest. An ANCOVA takes one continuous outcome from two or more separate groups, plus a continuous covariate such as a pretest, and tests whether the groups' means differ once the covariate is accounted for.
- MANOVA MANOVA compares groups on several related outcomes at once. A one-way MANOVA takes two or more related continuous outcomes from two or more separate groups and tests whether the groups' averages differ on the outcomes taken together.
- MANCOVA MANCOVA compares groups on several outcomes at once, adjusting for covariates. A MANCOVA takes two or more continuous outcomes from separate groups and tests whether the groups differ on the outcomes considered together, after adjusting for one or more covariates.
Linear Regression
Predicting a continuous outcome from one or more predictors.
- Simple Linear Regression Simple linear regression predicts one variable from another with a straight line. Simple linear regression takes one continuous predictor and one continuous outcome, finds the straight line with the smallest total squared prediction error, and tests whether its slope differs from zero.
- Multiple Linear Regression Multiple regression predicts an outcome from several predictors at once. Multiple linear regression takes several predictors and one continuous outcome and tests how well they predict it together, and what each predictor adds while holding the others constant.
- Hierarchical Regression Hierarchical regression tests whether each added block of predictors improves prediction. Hierarchical regression enters predictors in blocks, in an order the researcher sets in advance, and tests whether each new block improves the prediction of a continuous outcome beyond the blocks before it.
- Multivariate Regression Multivariate regression predicts several related outcomes from the same predictors. Multivariate regression takes several related continuous outcomes and regresses them all on the same predictors, testing whether each predictor matters for the outcomes as a set.
- Stepwise Regression Stepwise regression picks predictors automatically, one at a time, by p-value. Stepwise regression takes one continuous outcome and a pool of candidate predictors, then adds or drops predictors one at a time, keeping those that pass a p-value cutoff.
- Mediation Analysis Mediation analysis tests whether an effect runs through a middle variable. Mediation analysis takes a predictor, a proposed mediator and an outcome measured on the same people, and tests whether part of the predictor's link with the outcome runs through the mediator.
- Moderation Analysis Moderation analysis tests whether a relationship changes depending on a third variable. Moderation analysis takes a predictor, a moderator and a continuous outcome and tests whether the predictor's relationship with the outcome differs across levels of the moderator, using their product in a regression.
Generalized and Multilevel Regression
Regression for nested data and non-continuous outcomes.
- Multivariate Regression Multivariate regression predicts several related outcomes from the same predictors. Multivariate regression takes several related continuous outcomes and regresses them all on the same predictors, testing whether each predictor matters for the outcomes as a set.
- Multilevel Regression (HLM) Multilevel regression predicts an outcome for people nested in groups, like classrooms. Multilevel regression takes a continuous outcome from people nested in groups, such as students in classrooms, and tests predictors at both levels while accounting for how much group members resemble each other.
- Logistic Regression Logistic regression predicts a yes/no outcome from one or more predictors. Logistic regression takes a yes/no outcome and one or more predictors of any type and tests how the odds of the outcome differ with each predictor, holding the others constant.
- Multilevel Logistic Regression Multilevel logistic regression predicts a yes/no outcome for people nested in groups. Multilevel logistic regression takes a yes/no outcome for people nested in groups and tests how predictors at both levels relate to the odds, while estimating how much the groups differ.
- Multinomial Regression Multinomial regression predicts which of several unordered categories someone falls into. Multinomial regression takes an outcome with three or more unordered categories and tests how the odds of each category, compared with a chosen baseline category, differ with one or more predictors.
- Ordinal Regression Ordinal regression predicts an ordered outcome, like a rating. Ordinal regression takes an ordered outcome, such as a rating from very poor to very good, and tests whether one or more predictors go with its higher or lower categories.
- Poisson Regression Poisson regression predicts a count, like how often something happens. Poisson regression takes a count outcome, such as how many panic attacks someone has, and tests how one or more predictors relate to the rate at which the events happen.
- Generalized Estimating Equations (GEE) GEE estimates average effects on outcomes measured repeatedly or in clusters. Generalized estimating equations take an outcome measured repeatedly or in clusters, such as yes/no answers at several check-ins, and test how the population's average outcome differs with the predictors, allowing for correlation within clusters.
- Multilevel Growth-Curve Modeling Multilevel growth modeling describes each person's change over time and predicts it. Multilevel growth-curve modeling takes repeated scores from the same people, fits a line through each person's scores over time, and tests how the average line changes and what predicts people's rates of change.
Structural Equation Modeling
Testing systems of relationships among variables.
- Path Analysis Path analysis tests a diagram of how measured variables affect each other. Path analysis takes several measured variables and a diagram of which affect which, estimates every arrow at once, and tests whether the arrows left out are needed.
- Multilevel SEM Multilevel SEM tests relationships separately within groups and between groups. Multilevel structural equation modeling takes people nested in groups and splits each variable into a within-group and a between-group part, then estimates and tests paths at each level.
- Growth-Curve Modeling A growth curve model describes how people change over time. A latent growth curve model takes the same people's scores on three or more occasions and estimates their average trajectory and how much people differ in where they start and how fast they change.
Longitudinal and Growth Models
Modeling change over time.
- Growth-Curve Modeling A growth curve model describes how people change over time. A latent growth curve model takes the same people's scores on three or more occasions and estimates their average trajectory and how much people differ in where they start and how fast they change.
- Multilevel Growth-Curve Modeling Multilevel growth modeling describes each person's change over time and predicts it. Multilevel growth-curve modeling takes repeated scores from the same people, fits a line through each person's scores over time, and tests how the average line changes and what predicts people's rates of change.
Factor Analysis
Finding the latent dimensions behind a set of items.
- Exploratory Factor Analysis (EFA) Exploratory factor analysis finds the underlying factors that explain how items correlate. Exploratory factor analysis takes a set of items and finds how many common factors best account for their correlations, which items go with which factor, and how strongly.
- Confirmatory Factor Analysis (CFA) CFA tests whether items fit a factor structure you specified in advance. Confirmatory factor analysis takes a set of items and a structure named in advance, which items reflect which underlying traits, and tests how well that structure reproduces how the items go together.
- Average Variance Extracted (AVE) AVE measures how much of its items' variance a construct explains. Average variance extracted takes the loadings from a factor model and measures how much of its items' variance, on average, each construct accounts for.
Psychometrics and Measurement
Whether a measure measures what it should.
- Convergent Validity Convergent validity checks that a measure agrees with similar measures. Convergent validity asks whether a new measure agrees with established measures of the same construct, usually judged by how strongly their scores correlate and whether that beats correlations with other constructs.
- Discriminant Validity Discriminant validity checks that two scales measure different things. Discriminant validity takes two multi-item scales meant to measure different traits and asks whether they're distinct enough to count as two measures rather than one.
- Average Variance Extracted (AVE) AVE measures how much of its items' variance a construct explains. Average variance extracted takes the loadings from a factor model and measures how much of its items' variance, on average, each construct accounts for.
- Sensitivity and Specificity Sensitivity and specificity show how often a diagnostic test gets it right. Sensitivity and specificity take a yes/no test result and a reference-standard diagnosis for the same people and estimate how often the test correctly flags those who have the condition and clears those who don't.
- Item Analysis (Classical Test Theory) Item analysis checks each test item's difficulty and how well it works. Item analysis takes people's right-or-wrong answers to each item on a test and checks how hard each item is, how well it separates strong from weak test-takers, and how its wrong options behave.
- Item Response Theory (IRT) IRT models how answering each item depends on the trait being measured. Item response theory takes people's answers to a set of yes/no items and models how the chance of a yes on each item rises with the one trait they share.
- Differential Item Functioning (DIF) DIF checks whether an item favors one group at equal ability. The Mantel-Haenszel DIF procedure takes right-or-wrong item answers from two groups and tests, item by item, whether people with the same total score have different odds of answering correctly.
Classification and Diagnostic Analysis
Sorting cases into groups and judging how well a measure classifies.
- Cluster Analysis Cluster analysis sorts people into groups with similar profiles. Cluster analysis takes several measures from each person and sorts people into groups whose members have similar profiles, when the groups aren't known in advance.
- ROC Curve Analysis ROC analysis shows how well a score identifies people with a condition. ROC curve analysis takes a test score and a reference-standard diagnosis for the same people and shows how well the score separates those with and without the condition, across every possible cutoff.
Other Specialized Models
Models for specific kinds of data.
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…anxiety differed across the three groups, F(2, 87) = 4.12, p = .020, η2p = .09.
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