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A Reported Statistic

Read a result like F(2, 87) = 4.12, p = .020 and not sure what produced it? Paste it below, as the paper prints it. The Result Decoder reads each number back to you, names the tests that could have produced it, checks that the p-value fits the statistic, and says how big the effect is.

Result Decoder

Statistics by Symbol

Symbol	What It Is	Reported By
$z$	z Statistic A difference measured in standard errors, judged against the normal curve.	Cohen's Kappa · Fleiss' Kappa · Comparing Correlation Coefficients · Goodman and Kruskal's Gamma · Somers' D · z-Test for Proportions · Mann-Whitney U Test · Wilcoxon Signed-Rank Test · Logistic Regression · Multilevel Logistic Regression · Multinomial Regression · Ordinal Regression · Poisson Regression · Generalized Estimating Equations (GEE) · Path Analysis · Multilevel SEM · Growth-Curve Modeling
$t$	t Statistic A difference measured in standard errors.	Pearson Correlation · Spearman Correlation · Partial Correlation · One-Sample t-Test · Independent-Samples t-Test · Paired-Samples t-Test · Bayesian Independent-Samples t-Test · Simple Linear Regression · Multiple Linear Regression · Hierarchical Regression · Multivariate Regression · Mediation Analysis · Moderation Analysis · Multilevel Regression (HLM) · Multilevel Growth-Curve Modeling · Convergent Validity
$\chi^2$	Chi-Square Statistic A test statistic judged against a chi-square distribution. In a table, it adds up how far the observed counts sit from the counts the null hypothesis expects; in a model comparison, it measures how much worse the more constrained model fits.	Cramér's V · Contingency Coefficient · Pearson Chi-Square Test · McNemar's Test · Cochran's Q · Friedman Test · Multilevel Logistic Regression · Multinomial Regression · Poisson Regression · Path Analysis · Multilevel SEM · Growth-Curve Modeling · Confirmatory Factor Analysis (CFA) · Differential Item Functioning (DIF) · Markov Models
$F$	F Statistic The variance due to an effect divided by the error variance it is tested against.	One-Way Between-Subjects ANOVA · One-Way Repeated-Measures ANOVA · Factorial Between-Subjects ANOVA · Factorial Repeated-Measures ANOVA · Mixed Factorial ANOVA · Bayesian ANOVA · ANCOVA · MANOVA · MANCOVA · Multiple Linear Regression · Multivariate Regression · Stepwise Regression
$\eta^2_p$	Partial Eta Squared An effect's share of the variation, counting only that effect and its own error.	One-Way Repeated-Measures ANOVA · Factorial Between-Subjects ANOVA · Factorial Repeated-Measures ANOVA · Mixed Factorial ANOVA · ANCOVA · MANOVA · MANCOVA · Multivariate Regression
$\text{OR}$	Odds Ratio How many times higher the odds of an outcome are in one group than in another.	Fisher's Exact Test · McNemar's Test · Logistic Regression · Multilevel Logistic Regression · Multinomial Regression · Ordinal Regression · Generalized Estimating Equations (GEE)
$r^2$	Coefficient of Determination The share of the variation in one variable that lines up with another variable, or with a model's predictions.	Pearson Correlation · Simple Linear Regression · Multiple Linear Regression · Stepwise Regression · Multilevel Regression (HLM) · Multilevel SEM
$d$	Cohen's d A difference measured in standard deviations.	One-Sample t-Test · Independent-Samples t-Test · Paired-Samples t-Test · Bayesian Independent-Samples t-Test · Growth-Curve Modeling · Multilevel Growth-Curve Modeling
$V$	Cramér's V The strength of the association between two categorical variables, from 0 to 1.	Cramér's V · Contingency Coefficient · Pearson Chi-Square Test · Markov Models
$\eta^2_G$	Generalized Eta Squared An effect's share of the variation, counted the same way whatever the design, so it compares across designs.	One-Way Repeated-Measures ANOVA · Factorial Repeated-Measures ANOVA · Mixed Factorial ANOVA · ANCOVA
$\beta$	Standardized Coefficient A regression coefficient in standard deviations, comparable across predictors measured on different scales.	Multiple Linear Regression · Multilevel Regression (HLM) · Path Analysis · Multilevel SEM
$f^2$	Cohen's f² The variance the predictors predict relative to the variance they leave unpredicted; the effect size for a regression's F test.	Multiple Linear Regression · Hierarchical Regression · Moderation Analysis
$\text{CFI}$	Comparative Fit Index How much better a model fits than a model in which the measures are unrelated, from 0 to 1.	Path Analysis · Growth-Curve Modeling · Confirmatory Factor Analysis (CFA)
$r$	Pearson's r The strength and direction of a straight-line relationship, from −1 to 1.	Pearson Correlation · Simple Linear Regression · Convergent Validity
$V$	Pillai's Trace How much of the variation in several outcomes, taken together, lines up with the groups; the most robust MANOVA statistic.	MANOVA · MANCOVA · Multivariate Regression
$\text{RMSEA}$	Root Mean Square Error of Approximation How much a model misfits per degree of freedom, adjusted for sample size; 0 means no more misfit than chance.	Path Analysis · Growth-Curve Modeling · Confirmatory Factor Analysis (CFA)
$\text{SRMR}$	Standardized Root Mean Square Residual The typical gap between the observed correlations and the ones the model predicts.	Path Analysis · Growth-Curve Modeling · Confirmatory Factor Analysis (CFA)
$R^2_{\text{adj}}$	Adjusted R Squared R squared corrected for the number of predictors, as an estimate of the share of variance the predictors would predict in the population.	Multiple Linear Regression · Stepwise Regression
$h$	Cohen's h The difference between two proportions, or between one proportion and a fixed value, on a stretched (arcsine) scale that makes differences about equally easy to detect at any baseline.	z-Test for Proportions · Binomial Test
$\eta^2$	Eta Squared The share of the variation in an outcome that lines up with group membership.	One-Way Between-Subjects ANOVA · Bayesian ANOVA
$\chi^2$	Likelihood-Ratio Test A test of whether a larger model fits better than a smaller one nested inside it, from the drop in deviance.	Logistic Regression · Ordinal Regression
$R^2$	Pseudo-R² One of several stand-ins for R² in models of yes/no or categorical outcomes; none is a share of variance explained.	Logistic Regression · Multinomial Regression
$r_{rb}$	Rank-Biserial Correlation The share of comparisons that favor one side minus the share that favor the other, from −1 to 1.	Mann-Whitney U Test · Wilcoxon Signed-Rank Test
$\Lambda$	Wilks' Lambda The share of variation in several outcomes, taken together, that the groups leave unexplained.	MANOVA · MANCOVA
$\tilde{V}$	Bias-Corrected Cramér's V Cramér's V with its small-sample overestimate reduced.	Cramér's V
$\Delta R^2$	Change in R² How much more of the outcome's variation a model predicts after new predictors are added.	Moderation Analysis
$q$	Cohen's q The difference between two correlations after each is converted to Fisher's z.	Comparing Correlation Coefficients
$ab_{cs}$	Completely Standardized Indirect Effect The indirect effect in standard deviations of the outcome per standard deviation of the predictor.	Mediation Analysis
$C$	Contingency Coefficient Pearson's chi-square-based measure of association between two categorical variables, from 0 up to a ceiling below 1.	Contingency Coefficient
$C^{*}$	Corrected Contingency Coefficient The contingency coefficient divided by the largest value it could reach in a table that size, so it runs from 0 to 1.	Contingency Coefficient
$r_1 - r_2$	Difference between Correlations One group's correlation minus another's, in correlation units.	Convergent Validity
$r_c$	Disattenuated Correlation A correlation corrected for measurement error, estimating how strongly the true scores are related.	Convergent Validity
$\varepsilon$	Epsilon (Sphericity Correction) How close repeated-measures data come to sphericity, from 1 (perfect) down to 1/(k − 1).	One-Way Repeated-Measures ANOVA
$\varepsilon^2$	Epsilon Squared The share of the variation in ranks that lines up with group membership.	Kruskal-Wallis Test
$F_{\text{change}}$	F Change An F test of whether new predictors explain more of the outcome than chance alone would add.	Hierarchical Regression
$\gamma$	Goodman and Kruskal's Gamma The share of untied pairs that line up in the same order minus the share that go opposite ways, from −1 to 1.	Goodman and Kruskal's Gamma
$T^2$	Hotelling's T² The multivariate version of a squared t statistic, combining several outcomes' tests into one.	Multivariate Regression
$\text{IRR}$	Incidence Rate Ratio How many times higher one group's rate of events is than another's, holding the other predictors constant.	Poisson Regression
$W$	Kendall's W How consistently people put the same conditions in the same order, from 0 to 1.	Friedman Test
$W$	Kendall's W for Cochran's Q Cochran's Q divided by the largest value it could reach, from 0 to 1; Kendall's W for yes/no answers.	Cochran's Q
$D$	Kolmogorov-Smirnov D The largest gap between the share of scores at or below each value and the share a named distribution predicts.	Distribution Fitting
$H$	Kruskal-Wallis H How far groups' mean ranks spread from the middle rank, compared with chance.	Kruskal-Wallis Test
$\rho_{\text{latent}}$	Latent-Variable ICC The share of the variation in an underlying propensity that lies between clusters, for a yes/no outcome.	Multilevel Logistic Regression
$\Delta_{MH}$	MH D-DIF (ETS Delta Scale) The Mantel-Haenszel odds ratio rescaled to ETS's delta scale of item difficulty; negative values mean the item is harder for the focal group.	Differential Item Functioning (DIF)
$U$	Mann-Whitney U How many times a score from one group beats a score from the other.	Mann-Whitney U Test
$\text{MOR}$	Median Odds Ratio The typical odds ratio between two identical people in two randomly chosen clusters.	Multilevel Logistic Regression
$R^2_{\text{new}}$	Out-of-Sample R² The share of variation a model's fixed equation predicts in data it wasn't built from.	Stepwise Regression
$r_{xy \cdot z}$	Partial Correlation The correlation between two variables once a third variable's straight-line part has been removed from both.	Partial Correlation
$\hat{p}$	Predicted Probability The chance of the outcome that a model gives someone with particular predictor values.	Multinomial Regression
$sr$	Semipartial Correlation The correlation between one variable and the part of another that a control variable can't predict.	Partial Correlation
$W$	Shapiro-Wilk W How closely sorted scores line up with what a normal distribution expects, from near 0 to 1.	Distribution Fitting
$d_{YX}$	Somers' d How well one ordered variable predicts the order of another, from −1 to 1; it changes if you swap which is the predictor.	Somers' D
$r_s$	Spearman's Rho The strength and direction of a monotonic relationship, from −1 to 1; Pearson's r computed on ranks.	Spearman Correlation
$T$	Wilcoxon Signed-Rank Statistic The sum of the ranks of the positive difference scores.	Wilcoxon Signed-Rank Test

Other Ways to Start

Your Research Question You have a question you want answered: “Do students who sleep less score lower on exams?” Find Your Question Describe Your Study You have a study design, but no method yet: Three groups · different people in each · one score out of 100 Describe Your Study A Kind of Analysis You have a rough idea of the analysis: “It's some kind of correlation.” Browse by Kind All Methods You have a method's name: “My advisor said to run a mixed ANOVA.” Find the Method Glossary You have a term you don't recognize: “What's a Greenhouse-Geisser correction?” Look It Up