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.

gghistostats and ggdotplotstats

parametric

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]

non-parametric

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]

robust

Test: One-sample percentile bootstrap test
Effect size: robust location measure

ggwithinstats - 2 groups

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]

non-parametric

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]

robust

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/web/packages/WRS2/vignettes/WRS2.pdf

ggwithinstats > 2 groups

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:

non-parametric

Test: Friedman’s rank sum test
Effect size: Kendall’s W 0 (no agreement) to 1 (complete agreement)

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]

robust

Test: Heteroscedastic one-way repeated measures ANOVA for trimmed means
Effect size: Not available 😭

ggbetweenstats - 2 groups

parametric

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]

non-parametric

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

robust

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/web/packages/WRS2/vignettes/WRS2.pdf

ggbetweenstats > 2 groups

parametric

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:

non-parametric

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

robust

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/web/packages/WRS2/vignettes/WRS2.pdf

ggpiestats and ggbarstats

association test - unpaired

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

association test - paired

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

goodness-of-fit test

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

ggscatterstats and ggcorrmat

parametric

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]

non-parametric

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]

robust

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]

Suggestions

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