# How do you interpret the MSe and partial eta squared reported with an F-statistic?

In my area of psychology we report the results of a repeated measures ANOVA with 1 within subjects independent variable as follows:

F(2,60) = 120.29, MSe = 173.09, p<0.05, ηp2 = 0.78

I understand this results means that the main effect of the independent variable was significant, but what do the MSe and ηp2 each tell us? What would be considered "good" values for these terms?

Thanks!

## 1 Answer

The outputs of statistical analyses are not "good" or "bad", except that they are definitely bad no matter what numbers you get if you've done your analyses incorrectly, and good if you've chosen an appropriate model, gathered enough data, and avoided statistical pitfalls like p-hacking.

1. Always report actual p-values, rather than "p<0.05". The only exception is for very small p-values (e.g., p<0.0001).

2. MSE, the mean squared error, is not easy to interpret by itself. Its range of values completely depends on your measurement scale. For models fit to the same data, a smaller MSE is "better", but it's more complicated than that and there are better methods for model selection (but also problems with model selection generally).

3. Effect sizes like the partial eta squared depend entirely on the field and type of data being analyzed. Effect sizes that are large in one context may be considered small in another. Partial eta squared measures how much variance is explained by your predictor divided by how much variance is unexplained (plus the numerator), so values closer to 1 mean a bigger effect. 0.78 is usually quite a large effect in psychology, since many measures in psychology depend on individual factors that are hard to capture. Again, however, that isn't necessarily true in every single case.