pingouin.pairwise_gameshowell

pingouin.pairwise_gameshowell(data=None, dv=None, between=None, effsize='hedges')[source]

Pairwise Games-Howell post-hoc test.

Parameters
datapandas.DataFrame

DataFrame

dvstring

Name of column containing the dependent variable.

between: string

Name of column containing the between factor.

effsizestring or None

Effect size type. Available methods are:

• 'none': no effect size

• 'cohen': Unbiased Cohen d

• 'hedges': Hedges g

• 'r': Pearson correlation coefficient

• 'eta-square': Eta-square

• 'odds-ratio': Odds ratio

• 'AUC': Area Under the Curve

• 'CLES': Common Language Effect Size

Returns
statspandas.DataFrame

Stats summary:

• 'A': Name of first measurement

• 'B': Name of second measurement

• 'mean(A)': Mean of first measurement

• 'mean(B)': Mean of second measurement

• 'diff': Mean difference (= mean(A) - mean(B))

• 'se': Standard error

• 'T': T-values

• 'df': adjusted degrees of freedom

• 'pval': Games-Howell corrected p-values

• 'hedges': Hedges effect size (or any effect size defined in effsize)

Notes

Games-Howell [1] is very similar to the Tukey HSD post-hoc test but is much more robust to heterogeneity of variances. While the Tukey-HSD post-hoc is optimal after a classic one-way ANOVA, the Games-Howell is optimal after a Welch ANOVA. Please note that Games-Howell is not valid for repeated measures ANOVA. Only one-way ANOVA design are supported.

Compared to the Tukey-HSD test, the Games-Howell test uses different pooled variances for each pair of variables instead of the same pooled variance.

The T-values are defined as:

$t = \frac{\overline{x}_i - \overline{x}_j} {\sqrt{(\frac{s_i^2}{n_i} + \frac{s_j^2}{n_j})}}$

and the corrected degrees of freedom are:

$v = \frac{(\frac{s_i^2}{n_i} + \frac{s_j^2}{n_j})^2} {\frac{(\frac{s_i^2}{n_i})^2}{n_i-1} + \frac{(\frac{s_j^2}{n_j})^2}{n_j-1}}$

where $$\overline{x}_i$$, $$s_i^2$$, and $$n_i$$ are the mean, variance and sample size of the first group and $$\overline{x}_j$$, $$s_j^2$$, and $$n_j$$ the mean, variance and sample size of the second group.

The p-values are then approximated using the Studentized range distribution $$Q(\sqrt2|t_i|, r, v_i)$$.

Caution

The p-values might be slightly different than those obtained with R or Matlab because Pingouin uses the Gleason (1999) algorithm [2] for the studentized range approximation, which is more efficient and accurate.

References

1

Games, Paul A., and John F. Howell. “Pairwise multiple comparison procedures with unequal n’s and/or variances: a Monte Carlo study.” Journal of Educational Statistics 1.2 (1976): 113-125.

2

Gleason, John R. “An accurate, non-iterative approximation for studentized range quantiles.” Computational statistics & data analysis 31.2 (1999): 147-158.

Examples

Pairwise Games-Howell post-hocs on the Penguins dataset.

>>> import pingouin as pg