# 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

# Summary of tests and effect sizes

## two_sample_test + oneway_anova

No. of groups: 2 => two_sample_test
No. of groups: > 2 => oneway_anova

### between-subjects

Following (between-subjects) tests are carried out for each type of analyses-

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
Bayes Factor > 2 Fisher’s ANOVA BayesFactor::anovaBF
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

Following effect sizes (and confidence intervals/CI) are available for each type of test-

Type No. of groups Effect size CI? Function used
Parametric > 2 $$\eta_{p}^2$$, $$\omega_{p}^2$$ effectsize::omega_squared, effectsize::eta_squared
Non-parametric > 2 $$\epsilon_{ordinal}^2$$ effectsize::rank_epsilon_squared
Robust > 2 $$\xi$$ (Explanatory measure of effect size) WRS2::t1way
Bayes Factor > 2 $$R_{posterior}^2$$ performance::r2_bayes
Parametric 2 Cohen’s d, Hedge’s g effectsize::cohens_d, effectsize::hedges_g
Non-parametric 2 r (rank-biserial correlation) effectsize::rank_biserial
Robust 2 $$\xi$$ (Explanatory measure of effect size) WRS2::yuen.effect.ci
Bayesian 2 $$\delta_{posterior}$$ bayestestR::describe_posterior

### within-subjects

Following (within-subjects) tests are carried out for each type of analyses-

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
Bayes Factor > 2 One-way repeated measures ANOVA BayesFactor::anovaBF
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

Following effect sizes (and confidence intervals/CI) are available for each type of test-

Type No. of groups Effect size CI? Function used
Parametric > 2 $$\eta_{p}^2$$, $$\omega_{p}^2$$ effectsize::omega_squared, effectsize::eta_squared
Non-parametric > 2 $$W_{Kendall}$$ (Kendall’s coefficient of concordance) effectsize::kendalls_w
Robust > 2 $$\delta_{R-avg}^{AKP}$$ Algina-Keselman-Penfield robust standardized difference average
Bayes Factor > 2 $$R_{posterior}^2$$ performance::r2_bayes
Parametric 2 Cohen’s d, Hedge’s g effectsize::cohens_d, effectsize::hedges_g
Non-parametric 2 r (rank-biserial correlation) effectsize::rank_biserial
Robust 2 $$\delta_{R}^{AKP}$$ (Algina-Keselman-Penfield robust standardized difference) WRS2::dep.effect
Bayesian 2 $$\delta_{posterior}$$ bayestestR::describe_posterior

## one_sample_test

Following tests are carried out for each type of analyses-

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 trimcibt (custom)
Bayesian One-sample Student’s t-test BayesFactor::ttestBF

Following effect sizes (and confidence intervals/CI) are available for each type of test-

Type Effect size CI? Function used
Parametric Cohen’s d, Hedge’s g effectsize::cohens_d, effectsize::hedges_g
Non-parametric r (rank-biserial correlation) effectsize::rank_biserial
Robust trimmed mean trimcibt (custom)
Bayes Factor $$\delta_{posterior}$$ bayestestR::describe_posterior

## corr_test

Following tests are carried out for each type of analyses. Additionally, the correlation coefficients (and their confidence intervals) are used as effect sizes-

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

## contingency_table

Following tests are carried out for each type of analyses-

Type of data Design Test Function used
Unpaired $$n \times p$$ contingency table Pearson’s $$\chi^2$$ test stats::chisq.test
Paired $$n \times p$$ contingency table McNemar’s $$\chi^2$$ test stats::mcnemar.test
Frequency $$n \times 1$$ contingency table Goodness of fit ($$\chi^2$$ test) stats::chisq.test

Following effect sizes (and confidence intervals/CI) are available for each type of test-

Test Effect size CI? Function used
Pearson’s $$\chi^2$$ test Cramer’s $$V$$ effectsize::cramers_v
McNemar’s test Cohen’s $$g$$ effectsize::cohens_g
Goodness of fit Cramer’s $$V$$ effectsize::cramers_v

## meta_analysis

Type Test Effect size CI? Function used
Parametric Meta-analysis via random-effects models $$\beta$$ metafor::metafor
Robust Meta-analysis via robust random-effects models $$\beta$$ metaplus::metaplus
Bayes Meta-analysis via Bayesian random-effects models $$\beta$$ 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

# Dataframe as output

Although the primary focus of this package is to get expressions containing statistical results, one can also use it to extract dataframes containing these details.

For a more detailed summary of these dataframe: https://indrajeetpatil.github.io/statsExpressions//articles/web_only/dataframe_outputs.html

# Suggestions

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