pingouin.compute_effsize

pingouin.
compute_effsize
(x, y, paired=False, eftype='cohen')[source] Calculate effect size between two set of observations.
 Parameters
 xnp.array or list
First set of observations.
 ynp.array or list
Second set of observations.
 pairedboolean
If True, uses Cohen davg formula to correct for repeated measurements (see Notes).
 eftypestring
Desired output effect size. Available methods are:
'none'
: no effect size'cohen'
: Unbiased Cohen d'hedges'
: Hedges g'glass'
: Glass delta'r'
: correlation coefficient'etasquare'
: Etasquare'oddsratio'
: Odds ratio'AUC'
: Area Under the Curve'CLES'
: Common Language Effect Size
 Returns
 effloat
Effect size
See also
convert_effsize
Conversion between effect sizes.
compute_effsize_from_t
Convert a Tstatistic to an effect size.
Notes
Missing values are automatically removed from the data. If
x
andy
are paired, the entire row is removed.If
x
andy
are independent, the Cohen \(d\) is:\[d = \frac{\overline{X}  \overline{Y}} {\sqrt{\frac{(n_{1}  1)\sigma_{1}^{2} + (n_{2}  1) \sigma_{2}^{2}}{n1 + n2  2}}}\]If
x
andy
are paired, the Cohen \(d_{avg}\) is computed:\[d_{avg} = \frac{\overline{X}  \overline{Y}} {\sqrt{\frac{(\sigma_1^2 + \sigma_2^2)}{2}}}\]The Cohenâ€™s d is a biased estimate of the population effect size, especially for small samples (n < 20). It is often preferable to use the corrected Hedges \(g\) instead:
\[g = d \times (1  \frac{3}{4(n_1 + n_2)  9})\]The Glass \(\delta\) is calculated using the group with the lowest variance as the control group:
\[\delta = \frac{\overline{X}  \overline{Y}}{\sigma^2_{\text{control}}}\]The common language effect size is the proportion of pairs where
x
is higher thany
(calculated with a bruteforce approach where each observation ofx
is paired to each observation ofy
, seepingouin.wilcoxon()
for more details):\[\text{CL} = P(X > Y) + .5 \times P(X = Y)\]For other effect sizes, Pingouin will first calculate a Cohen \(d\) and then use the
pingouin.convert_effsize()
to convert to the desired effect size.References
Lakens, D., 2013. Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for ttests and ANOVAs. Front. Psychol. 4, 863. https://doi.org/10.3389/fpsyg.2013.00863
Cumming, Geoff. Understanding the new statistics: Effect sizes, confidence intervals, and metaanalysis. Routledge, 2013.
Examples
Cohen d from two independent samples.
>>> import numpy as np >>> import pingouin as pg >>> x = [1, 2, 3, 4] >>> y = [3, 4, 5, 6, 7] >>> pg.compute_effsize(x, y, paired=False, eftype='cohen') 1.707825127659933
The sign of the Cohen d will be opposite if we reverse the order of
x
andy
:>>> pg.compute_effsize(y, x, paired=False, eftype='cohen') 1.707825127659933
Hedges g from two paired samples.
>>> x = [1, 2, 3, 4, 5, 6, 7] >>> y = [1, 3, 5, 7, 9, 11, 13] >>> pg.compute_effsize(x, y, paired=True, eftype='hedges') 0.8222477210374874
3. Glass delta from two independent samples. The group with the lowest variance will automatically be selected as the control.
>>> pg.compute_effsize(x, y, paired=False, eftype='glass') 1.3887301496588271
Common Language Effect Size.
>>> pg.compute_effsize(x, y, eftype='cles') 0.2857142857142857
In other words, there are ~29% of pairs where
x
is higher thany
, which means that there are ~71% of pairs wherex
is lower thany
. This can be easily verified by changing the order ofx
andy
:>>> pg.compute_effsize(y, x, eftype='cles') 0.7142857142857143