Test and effect size details

This vignette can be cited as:

To cite package 'statsExpressions' in publications use:

  Patil, I., (2021). statsExpressions: R Package for Tidy Dataframes
  and Expressions with Statistical Details. Journal of Open Source
  Software, 6(61), 3236, https://doi.org/10.21105/joss.03236

A BibTeX entry for LaTeX users is

  @Article{,
    doi = {10.21105/joss.03236},
    year = {2021},
    publisher = {{The Open Journal}},
    volume = {6},
    number = {61},
    pages = {3236},
    author = {Indrajeet Patil},
    title = {{statsExpressions: {R} Package for Tidy Dataframes and Expressions with Statistical Details}},
    journal = {{Journal of Open Source Software}},
  }

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 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()

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()
Bayes Factor > 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()
Bayes Factor > 2 Bayesian R-squared Yes performance::r2_bayes()

within-subjects

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()
Bayes Factor > 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()
Bayes Factor > 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

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()
Bayes Factor 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::metafor()
Robust Meta-analysis via robust random-effects models beta Yes metaplus::metaplus()
Bayes 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

Suggestions

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