This vignette provides a go-to summary for which test is carried out for each function included in the package and what effect size it returns. Additionally, there are also recommendations on how to interpret those effect sizes.

Note that the following recommendations on how to interpret the effect sizes are just suggestions and there is nothing universal about them. The interpretation of **any** effect size measures is always going to be relative to the discipline, the specific data, and the aims of the analyst. Here the guidelines are given for *small*, *medium*, and *large* effects and references should shed more information on the baseline discipline with respect to which these guidelines were recommended. This is important because what might be considered a small effect in psychology might be large for some other field like public health.

`expr_t_onesample`

**Test**: One-sample *t*-test

**Effect size**: Cohen’s *d*, Hedge’s *g*

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

Cohen’s d |
0 – < 0.20 | 0.20 – < 0.50 | ≥ 0.80 | [0,1] |

Hedge’s g |
0 – < 0.20 | 0.20 – < 0.50 | ≥ 0.80 | [0,1] |

**Test**: One-sample Wilcoxon Signed-rank Test

**Effect size**: *r* ( = \(Z/\sqrt(N_{obs})\))

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

r |
0.10 – < 0.30 | 0.30 – < 0.50 | ≥ 0.50 | [0,1] |

**Test**: One-sample percentile bootstrap test

**Effect size**: robust location measure

`expr_t_parametric`

**Test**: Student’s dependent samples *t*-test

**Effect size**: Cohen’s *d*, Hedge’s *g*

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

Cohen’s d |
0.20 | 0.50 | 0.80 | [0,1] |

Hedge’s g |
0.20 | 0.50 | 0.80 | [0,1] |

**Test**: Wilcoxon signed-rank test

**Effect size**: *r* ( = \(Z/\sqrt(N_{pairs})\))

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

r |
0.10 – < 0.30 | 0.30 – < 0.50 | ≥ 0.50 | [0,1] |

**Test**: Yuen’s dependent sample trimmed means *t*-test

**Effect size**: Explanatory measure of effect size (\(\xi\))

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

\(\xi\) | 0.10 – < 0.30 | 0.30 – < 0.50 | ≥ 0.50 | [0,1] |

**Reference**: https://CRAN.R-project.org/package=WRS2/vignettes/WRS2.pdf

**Test**: Student’s and Welch’s independent samples *t*-test

**Effect size**: Cohen’s *d*, Hedge’s *g*

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

Cohen’s d |
0.20 | 0.50 | 0.80 | [0,1] |

Hedge’s g |
0.20 | 0.50 | 0.80 | [0,1] |

**Test**: Two-sample Mann–Whitney *U* Test

**Effect size**: *r* ( = \(Z/\sqrt(N_{obs})\))

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

r |
0.10 – < 0.30 | 0.30 – < 0.50 | ≥ 0.50 | [0,1] |

**Reference**: https://rcompanion.org/handbook/F_04.html

**Test**: Yuen’s independent sample trimmed means *t*-test

**Effect size**: Explanatory measure of effect size (\(\xi\))

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

\(\xi\) | 0.10 – < 0.30 | 0.30 – < 0.50 | ≥ 0.50 | [0,1] |

**Reference**: https://CRAN.R-project.org/package=WRS2/vignettes/WRS2.pdf

`expr_anova_parametric`

**Test**: Fisher’s repeated measures one-way ANOVA

**Effect size**: \(\eta^2_p\), \(\omega^2\)

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

\(\omega^2\) | 0.01 – < 0.06 | 0.06 – < 0.14 | ≥ 0.14 | [0,1] |

\(\eta^2_p\) | 0.01 – < 0.06 | 0.06 – < 0.14 | ≥ 0.14 | [0,1] |

**Reference**:

**Test**: Friedman’s rank sum test

**Effect size**: Kendall’s *W*

In the following table, *k* is the number of treatments, groups, or things being rated.

k |
Small | Medium | Large | Range |
---|---|---|---|---|

k = 3 |
< 0.10 | 0.10 – < 0.30 | ≥ 0.30 | [0,1] |

k = 5 |
< 0.10 | 0.10 – < 0.25 | ≥ 0.25 | [0,1] |

k = 7 |
< 0.10 | 0.10 – < 0.20 | ≥ 0.20 | [0,1] |

k = 9 |
< 0.10 | 0.10 – < 0.20 | ≥ 0.20 | [0,1] |

**Test**: Heteroscedastic one-way repeated measures ANOVA for trimmed means

**Effect size**: Not available

**Test**: Fisher’s or Welch’s one-way ANOVA

**Effect size**: \(\eta^2\), \(\eta^2_p\), \(\omega^2\), \(\omega^2_p\)

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

\(\eta^2\) | 0.01 – < 0.06 | 0.06 – < 0.14 | ≥ 0.14 | [0,1] |

\(\omega^2\) | 0.01 – < 0.06 | 0.06 – < 0.14 | ≥ 0.14 | [0,1] |

\(\eta^2_p\) | 0.01 – < 0.06 | 0.06 – < 0.14 | ≥ 0.14 | [0,1] |

\(\omega^2_p\) | 0.01 – < 0.06 | 0.06 – < 0.14 | ≥ 0.14 | [0,1] |

**Reference**:

**Test**: Kruskal–Wallis test

**Effect size**: \(\epsilon^2\)

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

\(\epsilon^2\) | 0.01 – < 0.08 | 0.08 – < 0.26 | ≥ 0.26 | [0,1] |

**Reference**: https://rcompanion.org/handbook/F_08.html

**Test**: Heteroscedastic one-way ANOVA for trimmed means

**Effect size**: Explanatory measure of effect size (\(\xi\))

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

\(\xi\) | 0.10 – < 0.30 | 0.30 – < 0.50 | ≥ 0.50 | [0,1] |

**Reference**: https://CRAN.R-project.org/package=WRS2/vignettes/WRS2.pdf

`expr_contingency_tab`

**Test**: Pearson’s \(\chi^2\)-squared test

**Effect size**: Cramér’s *V*

In the following table, *k* is the minimum number of categories in either rows or columns.

k |
Small | Medium | Large | Range |
---|---|---|---|---|

k = 2 |
0.10 – < 0.30 | 0.30 – < 0.50 | ≥ 0.50 | [0,1] |

k = 3 |
0.07 – < 0.20 | 0.20 – < 0.35 | ≥ 0.35 | [0,1] |

k = 4 |
0.06 – < 0.17 | 0.17 – < 0.29 | ≥ 0.29 | [0,1] |

**Reference**: https://rcompanion.org/handbook/H_10.html

**Test**: McNemar’s test

**Effect size**: Cohen’s *g*

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

Cohen’s g |
0.05 – < 0.15 | 0.15 – < 0.25 | ≥ 0.25 | [0,1] |

**Reference**: https://rcompanion.org/handbook/H_05.html

**Test**: Pearson’s \(\chi^2\)-squared goodness-of-fit test

**Effect size**: Cramér’s *V*

In the following table, *k* is the number of categories.

k |
Small | Medium | Large | Range |
---|---|---|---|---|

k = 2 |
0.100 – < 0.300 | 0.300 – < 0.500 | ≥ 0.500 | [0,1] |

k = 3 |
0.071 – < 0.212 | 0.212 – < 0.354 | ≥ 0.354 | [0,1] |

k = 4 |
0.058 – < 0.173 | 0.173 – < 0.289 | ≥ 0.289 | [0,1] |

k = 5 |
0.050 – < 0.150 | 0.150 – < 0.250 | ≥ 0.250 | [0,1] |

k = 6 |
0.045 – < 0.134 | 0.134 – < 0.224 | ≥ 0.224 | [0,1] |

k = 7 |
0.043 – < 0.130 | 0.130 – < 0.217 | ≥ 0.217 | [0,1] |

k = 8 |
0.042 – < 0.127 | 0.127 – < 0.212 | ≥ 0.212 | [0,1] |

k = 9 |
0.042 – < 0.125 | 0.125 – < 0.209 | ≥ 0.209 | [0,1] |

k = 10 |
0.041 – < 0.124 | 0.124 – < 0.207 | ≥ 0.207 | [0,1] |

**Reference**: https://rcompanion.org/handbook/H_03.html

`expr_corr_test`

**Test**: Pearson product-moment correlation coefficient

**Effect size**: Pearson’s correlation coefficient (*r*)

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

Pearson’s r |
0.10 – < 0.30 | 0.30 – < 0.50 | ≥ 0.50 | [-1,1] |

**Test**: Spearman’s rank correlation coefficient

**Effect size**: Spearman’s rank correlation coefficient (\(\rho\))

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

Spearman’s \(\rho\) | 0.10 – < 0.30 | 0.30 – < 0.50 | ≥ 0.50 | [-1,1] |

**Test**: Percentage bend correlation coefficient

**Effect size**: Percentage bend correlation coefficient (\(\rho_{pb}\))

Effect size | Small | Medium | Large | Range |
---|---|---|---|---|

\(\rho_{pb}\) | 0.10 – < 0.30 | 0.30 – < 0.50 | ≥ 0.50 | [-1,1] |

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

For details, see- https://indrajeetpatil.github.io/ggstatsplot/articles/web_only/session_info.html