pingouin.pairwise_tukey#

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

Pairwise Tukey-HSD post-hoc test.

Parameters:
datapandas.DataFrame

DataFrame. Note that this function can also directly be used as a Pandas method, in which case this argument is no longer needed.

dvstring

Name of column containing the dependent variable.

betweenstring or list with N elements

Name of column(s) containing the between factor(s). If between is a list with two or more elements, all the combinations of levels (cells) of the factors are compared, i.e. the interaction term.

Changed in version 0.7.0: between can be a list of factors.

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

  • 'A': Name of first measurement (a tuple with one level per factor if between has several factors)

  • '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

  • 'p_tukey': Tukey-HSD corrected p-values

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

See also

pairwise_tests, pairwise_gameshowell

Notes

Tukey HSD post-hoc [1] is best for balanced one-way ANOVA.

It has been proven to be conservative for one-way ANOVA with unequal sample sizes. However, it is not robust if the groups have unequal variances, in which case the Games-Howell test is more adequate. Tukey HSD is not valid for repeated measures ANOVA.

With several between factors, the groups are all the observed combinations of levels of the factors, and \(\text{MS}_w\) is the residual of the full factorial ANOVA (with all the interactions). This is the same as TukeyHSD(aov(dv ~ A * B), which = "A:B") in R.

The T-values are defined as:

\[t = \frac{\overline{x}_i - \overline{x}_j} {\sqrt{2 \cdot \text{MS}_w / n}}\]

where \(\overline{x}_i\) and \(\overline{x}_j\) are the means of the first and second group, respectively, \(\text{MS}_w\) the mean squares of the error (computed using ANOVA) and \(n\) the sample size.

If the sample sizes are unequal, the Tukey-Kramer procedure is automatically used:

\[t = \frac{\overline{x}_i - \overline{x}_j}{\sqrt{\frac{MS_w}{n_i} + \frac{\text{MS}_w}{n_j}}}\]

where \(n_i\) and \(n_j\) are the sample sizes of the first and second group, respectively.

The p-values are then approximated using the Studentized range distribution \(Q(\sqrt2|t_i|, r, N - r)\) where \(r\) is the total number of groups and \(N\) is the total sample size.

References

[1]

Tukey, John W. “Comparing individual means in the analysis of variance.” Biometrics (1949): 99-114.

[2]

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

Examples

Pairwise Tukey post-hocs on the Penguins dataset.

>>> import pingouin as pg
>>> df = pg.read_dataset("penguins")
>>> df.pairwise_tukey(dv="body_mass_g", between="species").round(3)
           A          B    mean_A    mean_B      diff      se       T  p_tukey  hedges
0     Adelie  Chinstrap  3700.662  3733.088   -32.426  67.512  -0.480    0.881  -0.074
1     Adelie     Gentoo  3700.662  5076.016 -1375.354  56.148 -24.495    0.000  -2.860
2  Chinstrap     Gentoo  3733.088  5076.016 -1342.928  69.857 -19.224    0.000  -2.875

Tukey post-hocs on the interaction of species and sex, i.e. all the pairs of species x sex combinations. This is the same as TukeyHSD(aov(body_mass_g ~ species * sex), which = "species:sex") in R.

>>> stats = pg.pairwise_tukey(data=df, dv="body_mass_g", between=["species", "sex"])
>>> stats[["A", "B", "diff", "T", "p_tukey"]].head(4).round(3)
                  A                    B      diff       T  p_tukey
0  (Adelie, female)       (Adelie, male)  -674.658 -13.174    0.000
1  (Adelie, female)  (Chinstrap, female)  -158.370  -2.465    0.138
2  (Adelie, female)    (Chinstrap, male)  -570.135  -8.875    0.000
3  (Adelie, female)     (Gentoo, female) -1310.906 -24.088    0.000
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