Test and effect size details

Introduction

Here a go-to summary about statistical test carried out and the returned effect size for each function is provided. This should be useful if one needs to find out more information about how an argument is resolved in the underlying package or if one wishes to browse the source code. So, for example, if you want to know more about how one-way (between-subjects) ANOVA, you can run ?stats::oneway.test in your R console.

Abbreviations used: CI = Confidence Interval

Data requirements

All functions expect data in long (tidy) format — one row per observation. A few additional requirements are worth noting:

Within-subjects (repeated measures) designs: The data must contain exactly one observation per subject per condition (a complete, balanced block design). If you have multiple trials per subject-condition cell, aggregate them first (e.g., by taking the mean) before passing the data. You can verify this with table(data$subject, data$condition) — every cell should equal 1.
subject.id argument: For within-subjects designs, always specify subject.id explicitly. If omitted, the function pairs observations by row order within each condition, so any data that is not already sorted identically within every condition level can produce silently incorrect paired tests — even with exactly two conditions and no missing values.
Missing data: Missing values are handled internally by removing any subject who has NA in any condition, ensuring a balanced design is maintained.

Summary of functionality

Summary of available analyses

Test	Function
one-sample t-test	`one_sample_test()`
two-sample t-test	`two_sample_test()`
one-way ANOVA	`oneway_anova()`
correlation analysis	`corr_test()`
contingency table analysis	`contingency_table()`
meta-analysis	`meta_analysis()`
pairwise comparisons	`pairwise_comparisons()`
pairwise contingency table	`pairwise_contingency_table()`

Summary of details available for analyses

Analysis	Hypothesis testing	Effect size estimation
(one/two-sample) t-test	✅	✅
one-way ANOVA	✅	✅
correlation	✅	✅
(one/two-way) contingency table	✅	✅
random-effects meta-analysis	✅	✅

Summary of supported statistical approaches

Description	Parametric	Non-parametric	Robust	Bayesian
Between group/condition comparisons	✅	✅	✅	✅
Within group/condition comparisons	✅	✅	✅	✅
Distribution of a numeric variable	✅	✅	✅	✅
Correlation between two variables	✅	✅	✅	✅
Association between categorical variables	✅	✅	❌	✅
Equal proportions for categorical variable levels	✅	✅	❌	✅
Random-effects meta-analysis	✅	❌	✅	✅

Summary of tests and effect sizes

Here a go-to summary about statistical test carried out and the returned effect size for each function is provided. This should be useful if one needs to find out more information about how an argument is resolved in the underlying package or if one wishes to browse the source code. So, for example, if you want to know more about how one-way (between-subjects) ANOVA, you can run ?stats::oneway.test in your R console.

`centrality_description()`

Type	Measure	Function used
Parametric	mean	`datawizard::describe_distribution()`
Non-parametric	median	`datawizard::describe_distribution()`
Robust	trimmed mean	`datawizard::describe_distribution()`
Bayesian	MAP	`datawizard::describe_distribution()`

`oneway_anova()`

between-subjects

Hypothesis testing

Type	No. of groups	Test	Function used
Parametric	> 2	Fisher’s or Welch’s one-way ANOVA	`stats::oneway.test()`
Non-parametric	> 2	Kruskal-Wallis one-way ANOVA	`stats::kruskal.test()`
Robust	> 2	Heteroscedastic one-way ANOVA for trimmed means	`WRS2::t1way()`
Bayesian	> 2	Fisher’s ANOVA	`BayesFactor::anovaBF()`

Effect size estimation

Type	No. of groups	Effect size	CI available?	Function used
Parametric	> 2	partial eta-squared, partial omega-squared	Yes	`effectsize::omega_squared()`, `effectsize::eta_squared()`
Non-parametric	> 2	rank epsilon squared	Yes	`effectsize::rank_epsilon_squared()`
Robust	> 2	Explanatory measure of effect size	Yes	`WRS2::t1way()`
Bayesian	> 2	Bayesian R-squared	Yes	`performance::r2_bayes()`

within-subjects

Data requirement: Repeated measures tests assume a complete design with exactly one observation per subject per condition. If your data has multiple trials per cell, aggregate first (e.g., take the mean). Verify with table(data$subject, data$condition) — every cell should equal 1.

Hypothesis testing

Type	No. of groups	Test	Function used
Parametric	> 2	One-way repeated measures ANOVA	`afex::aov_ez()`
Non-parametric	> 2	Friedman rank sum test	`stats::friedman.test()`
Robust	> 2	Heteroscedastic one-way repeated measures ANOVA for trimmed means	`WRS2::rmanova()`
Bayesian	> 2	One-way repeated measures ANOVA	`BayesFactor::anovaBF()`

Effect size estimation

Type	No. of groups	Effect size	CI available?	Function used
Parametric	> 2	partial eta-squared, partial omega-squared	Yes	`effectsize::omega_squared()`, `effectsize::eta_squared()`
Non-parametric	> 2	Kendall’s coefficient of concordance	Yes	`effectsize::kendalls_w()`
Robust	> 2	Algina-Keselman-Penfield robust standardized difference average	Yes	`WRS2::wmcpAKP()`
Bayesian	> 2	Bayesian R-squared	Yes	`performance::r2_bayes()`

`two_sample_test()`

between-subjects

Hypothesis testing

Type	No. of groups	Test	Function used
Parametric	2	Student’s or Welch’s t-test	`stats::t.test()`
Non-parametric	2	Mann-Whitney U test	`stats::wilcox.test()`
Robust	2	Yuen’s test for trimmed means	`WRS2::yuen()`
Bayesian	2	Student’s t-test	`BayesFactor::ttestBF()`

Effect size estimation

Type	No. of groups	Effect size	CI available?	Function used
Parametric	2	Cohen’s d, Hedge’s g	Yes	`effectsize::cohens_d()`, `effectsize::hedges_g()`
Non-parametric	2	r (rank-biserial correlation)	Yes	`effectsize::rank_biserial()`
Robust	2	Algina-Keselman-Penfield robust standardized difference	Yes	`WRS2::akp.effect()`
Bayesian	2	difference	Yes	`bayestestR::describe_posterior()`

within-subjects

Data requirement: Paired tests assume exactly one observation per subject per condition. If your data has multiple trials per cell, aggregate first (e.g., take the mean).

Hypothesis testing

Type	No. of groups	Test	Function used
Parametric	2	Student’s t-test	`stats::t.test()`
Non-parametric	2	Wilcoxon signed-rank test	`stats::wilcox.test()`
Robust	2	Yuen’s test on trimmed means for dependent samples	`WRS2::yuend()`
Bayesian	2	Student’s t-test	`BayesFactor::ttestBF()`

Effect size estimation

Type	No. of groups	Effect size	CI available?	Function used
Parametric	2	Cohen’s d, Hedge’s g	Yes	`effectsize::cohens_d()`, `effectsize::hedges_g()`
Non-parametric	2	r (rank-biserial correlation)	Yes	`effectsize::rank_biserial()`
Robust	2	Algina-Keselman-Penfield robust standardized difference	Yes	`WRS2::wmcpAKP()`
Bayesian	2	difference	Yes	`bayestestR::describe_posterior()`

`one_sample_test()`

Hypothesis testing

Type	Test	Function used
Parametric	One-sample Student’s t-test	`stats::t.test()`
Non-parametric	One-sample Wilcoxon test	`stats::wilcox.test()`
Robust	Bootstrap-t method for one-sample test	`WRS2::trimcibt()`
Bayesian	One-sample Student’s t-test	`BayesFactor::ttestBF()`

Effect size estimation

Type	Effect size	CI available?	Function used
Parametric	Cohen’s d, Hedge’s g	Yes	`effectsize::cohens_d()`, `effectsize::hedges_g()`
Non-parametric	r (rank-biserial correlation)	Yes	`effectsize::rank_biserial()`
Robust	trimmed mean	Yes	`WRS2::trimcibt()`
Bayesian	difference	Yes	`bayestestR::describe_posterior()`

`corr_test()`

Hypothesis testing and Effect size estimation

Type	Test	CI available?	Function used
Parametric	Pearson’s correlation coefficient	Yes	`correlation::correlation()`
Non-parametric	Spearman’s rank correlation coefficient	Yes	`correlation::correlation()`
Robust	Winsorized Pearson’s correlation coefficient	Yes	`correlation::correlation()`
Bayesian	Bayesian Pearson’s correlation coefficient	Yes	`correlation::correlation()`

`contingency_table()`

two-way table

Hypothesis testing

Type	Design	Test	Function used
Parametric/Non-parametric	Unpaired	Pearson’s chi-squared test	`stats::chisq.test()`
Bayesian	Unpaired	Bayesian Pearson’s chi-squared test	`BayesFactor::contingencyTableBF()`
Parametric/Non-parametric	Paired	McNemar’s chi-squared test	`stats::mcnemar.test()`
Bayesian	Paired	No	No

Effect size estimation

Type	Design	Effect size	CI available?	Function used
Parametric/Non-parametric	Unpaired	Cramer’s V	Yes	`effectsize::cramers_v()`
Bayesian	Unpaired	Cramer’s V	Yes	`effectsize::cramers_v()`
Parametric/Non-parametric	Paired	Cohen’s g	Yes	`effectsize::cohens_g()`
Bayesian	Paired	No	No	No

one-way table

Hypothesis testing

Type	Test	Function used
Parametric/Non-parametric	Goodness of fit chi-squared test	`stats::chisq.test()`
Bayesian	Bayesian Goodness of fit chi-squared test	(custom)

Effect size estimation

Type	Effect size	CI available?	Function used
Parametric/Non-parametric	Pearson’s C	Yes	`effectsize::pearsons_c()`
Bayesian	No	No	No

`meta_analysis()`

Hypothesis testing and Effect size estimation

Type	Test	Effect size	CI available?	Function used
Parametric	Meta-analysis via random-effects models	beta	Yes	`metafor::rma()`
Robust	Meta-analysis via robust random-effects models	beta	Yes	`metaplus::metaplus()`
Bayesian	Meta-analysis via Bayesian random-effects models	beta	Yes	`metaBMA::meta_random()`

Effect size interpretation

See {effectsize}’s interpretation functions to check different rules/conventions to interpret effect sizes:

https://easystats.github.io/effectsize/reference/index.html#section-interpretation

References

For parametric and non-parametric effect sizes: https://easystats.github.io/effectsize/articles/
For robust effect sizes: https://CRAN.R-project.org/package=WRS2/vignettes/WRS2.pdf
For Bayesian posterior estimates: https://easystats.github.io/bayestestR/articles/bayes_factors.html

Suggestions

If you find any bugs or have any suggestions/remarks, please file an issue on GitHub: https://github.com/IndrajeetPatil/statsExpressions/issues