6) Why do we use partial eta squared instead of eta squared in relation to calcu

Question

6) Why do we use partial eta squared instead of eta squared in relation to calculating effect sizes in ANCOVA? Please explain exactly what variable(s) would be considered when using partial eta squared in ANCOVA. What does the partial eta squared calculation look like for the variable(s)?

7) Please use equation (e.g., Outcome = b0 +…+ ??i) to look at the effects of mindfulness (level à 1 = control; 2 = low mindfulness; 3 = high mindfulness) on stress levels (scale of 0-7) with the covariate being ‘ability to relax’ (scale of 0-10).

8) What are the two main reasons to include covariates in ANOVA?

Explanation / Answer

6) In a one-way ANCOVA, Eta Squared and Partial Eta Squared will be equal, but this isn’t true in models with more than one independent variable.

The drawback for Eta Squared is that it is a biased measure of population variance explained. It always overestimates it.

that “at least two formulas have been recently suggested for the purpose of calculating eta squared within an ANCOVA context”. Eta-squared (?²) and partial eta-squared (?p²) are biased effect size estimators.

The bias for ?², ?², and ?², for sample sizes of 10 to 100 per condition, for three effect sizes. we can uses small, medium, and large effect sizes, but I have run additional simulations for the now more commonly used small (?² = 0.0099), medium (?² = 0.0588), and large (?² = 0.1379) effects. but in a One-Way ANCOVA ?² = ?p².

When there is no true effect, ?² from small studies can easily give the wrong impression that there is a real small to medium effect, just due to the bias. Your p-value would not be statistically significant, but this overestimation could be problematic if you ignore the p-value and just focus on estimation.

So,  we use partial eta squared instead of eta squared in relation to calculating effect sizes in ANCOVA.

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