# Why does meanEffectSize() use sqrt((varX + varY)/2) for the paired cohensD calculation?

6 visualizzazioni (ultimi 30 giorni)
Samantha Michalka il 10 Giu 2023
I have typically seen Cohen's d for a paired data set calculated using the std(x-y), which is also the same as the std reported by running ttest(x,y). However, the meanEffectSize function appears to use stddev = sqrt((varX + varY)/2). The meanEffectSize function is giving me a different effect size than if I calculate it in the way I've typically seen. Does this alternate calculate relate to the use of hedgesCorrection or is it separate from this?
##### 0 CommentiMostra -2 commenti meno recentiNascondi -2 commenti meno recenti

Accedi per commentare.

### Risposta accettata

Ive J il 11 Giu 2023
Modificato: Ive J il 11 Giu 2023
I assume you mean (check more flavors in this paper):
x = [10 12 15 8 11];
y = [14 18 16 12 13];
d = mean(x-y)/std(x-y)
d = -1.7442
eff = meanEffectSize(x, y, "Paired", true, "Effect", "cohen")
eff = 1×2 table
Effect ConfidenceIntervals _______ ___________________ CohensD -1.0851 -2.906 -0.18213
And yes, you are correct, the difference is because of hedgesCorrection. Also apparently, the function considers within subject correlation. Let's check it in R with effsize::cohen.d
%# in R
% x = c(10 ,12, 15, 8, 11);
% y = c(14 ,18 ,16,12,13);
% effsize::cohen.d(x, y, paired = T, within = F, hedges.correction = F)
Cohen's d
d estimate: -1.744163 (large)
95 percent confidence interval:
lower upper
-3.3816056 -0.1067208
% effsize::cohen.d(x, y, paired = T, within = T, hedges.correction = T)
Hedges's g
g estimate: -1.084754 (large)
95 percent confidence interval:
lower upper
-1.8930902 -0.2764184
##### 1 CommentoMostra -1 commenti meno recentiNascondi -1 commenti meno recenti
Samantha Michalka il 14 Giu 2023

Accedi per commentare.

### Categorie

Scopri di più su Statistics and Machine Learning Toolbox in Help Center e File Exchange

R2022b

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by