Thank you Safa Aouinti

Partial eta square is a ratio of the SS for an effect to the SS for the error term plus the SS effect: SSeffect / (SSeffect + SSerror).

Thus it can't be interpreted (in general) as the proportion of variance explained in the sample by an effect (which would be eta-squared). Crucially in anything but a simple one factor between design it ignores SS due to all other factors and any random effects (such as participants) and error terms for other effects. This means for example partial eta square can sum to greater than 1. I'd argue therefore that it is next to useless for interpreting effect size (except in a few corner cases).

The best option (for eta-squared type measures) is probably generalised eta-square which tries to estimate what eta-squared would be in a between-subjects design by differentiating between manipulated an measures factors. Measured factors should be part of the denominator because they represent variability in the data that is likely to occur outside the experiment (e.g., due to gender) and manipulated factors are not because they create variance unique to that experiment.

It is a bit harder to calculate - so eta-squared has a fairly simple interpretation (the proportion of variance in your sample explained by the effect). Note also that all variance explained measures suffer from problems of interpretation (because you are scaling things relative to all sources of variability including measurement error and so forth) which might not be stable between studies or contexts.

Thank you Thom S Baguley

Can you tell me a short answer about the question. Is it possible to interpret the partial eta square in the "within-subjects effects" of repeated measures? Yes or no?

Not very easily. It is the proportion of variance in your data (not the population) once you exclude individual differences explained by the effect (assuming it is a one-way ANOVA).

The reason this isn't helpful is that in all relevant contexts which you want to try and interpret there will be individual differences so using partial eta-squared gives you a misleadingly large number if you are trying to estimate what proportion of variance is explained in practical terms. (The exception is for power calculations where you might just want the partial eta-squared).

The ANOVA output will give you enough information to calculate eta-squared (SS effect / SS total where SStotal simply adds up all SS from all effects and error terms) which has a simpler interpretation, though all variance explained measures have limitations.

Thom S Baguley thank you very much.

So we can not use partial eta square because "SS subjcet" is removed from the denominator of the formula.

There are always individual differences, so using partial eta square is meaningless. Why does SPSS use this criterion in its outputs?

It is a huge mystery as to why SPSS makes partial eta-squared its default. It has one main use - in power calculations. This is because the test of the effect does remove individual differences in a within subjects design. However, SPSS also messes that up by reporting "observed power" which is a nonsense.

The partial eta-squared statistic could be used to plan a replication with an identical design but does not tell you retrospectively about the power for the study it came from (which is arguable 0 or 1). If a replication uses a different design the partial eta-squared statistic might not be informative (e.g., if you did a between participant replication). In any case a power analysis should probably look at a range of plausible effect sizes of interest (because the estimate from a previous study will have sampling error etc.).

Thom S Baguley Thank you so much.

Thank you so much ! I was reading the paper of Levine et al (2002), so i thought the same "Why SPSS makes partial eta-squared as default?". So, you recommended to use a generalized eta-squared to report the effect size of a mixed (repeated measures) ANOVA?

I have a mixed ANOVA with 3 within-subject factor and one between-subject factor.

If you need standardized effect size based on sample variance explained then generalized eta-squared is my recommendation. I have a simplified formula for this in my book and some software (ez and afex packages in R can compute it if you specific which variables are manipulated/measured).

However, more generally I prefer interpret to interpreted unstandardised effect size (differences in means on the original scale).

Great! I'll look for your book, but i´m afraid I'll choose to report de differences in means too...

Thank you very much for answering!