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Effect size in a repeated-measures ANOVA

Reinaldo

Hi all,

I perform a repeated-measures ANOVA using Fit Model (Personality = Standard Least Squares; Emphasis = Minimal Report or Effect Leverage; Method =REML) and the Fit Least Squares report does not show the Sum of Squares of Model (SS_M) and Sum of Squares of Total Variance Amount (SS_T).

I need SS_M and SS_T to calculate the effect size (i.e., eta squared):

eta squared = SS_M / SS_T

Would you please help me to find those parameters (SS_M and SS_T)?

Thank you.

Accepted answers

cwillden

I suggested Fit Y by X because it does have an option to specify a Block column, which is a potential way to handle your repeat measures. The only conditions for Fit Y by X is the blocks have to be balanced and you can only have 1 treatment factor. If you're dead set on using REML, I don't know how to get the full ANOVA table from Fit Model with random effects. I don't think you can.

I guess you could work it out backwards by hand. The Fixed Effects test will give you the F-ratio and the numerator and denominator degrees of freedom. The MSE is in the variance components table. First, we need to solve for the treatment mean squares (let's call it MSM), and the total mean squares (MST).

To get MSM, multiply the F-ratio by MSE. Now, add MSM and MSE together to get MST.

Now, all that's left to do is multiply each of those by their respective degrees of freedom to get SSM and SST. SSM = MSM*DF (numerator degrees of freedom). SST = MST*(DF + DFDen).

To my understanding, computing the effect size from this approach makes it relative to the total variance remaining after accounting for random effects. If you want to calculate it relative to the total variance including random effects, you could compute SST on your response variable column with a column formula like Col Sum((:Y - Col Mean(:Y))^2).

All comments

cwillden

I'm not sure how to coerce that information out of Fit Model, but if it's a simple one-way ANOVA with repeated measures, you could use Fit Y by X with the subject ID as a blocking factor. When I tried it, I got an equivalent p-value for the treatment factor between Fit Y by X and Fit Model. Fit Y by X will provide the full ANOVA table, so you can compute eta^2.

Reinaldo

Hi @cwillden, thank you for your mail and information.

It seems the random effect (REML) is not considered in Fit Y by X. So, when I use Method = REML in a repeated-measures ANOVA, how could the effect size be calculated?

Thank you.

cwillden

To get MSM, multiply the F-ratio by MSE. Now, add MSM and MSE together to get MST.

Now, all that's left to do is multiply each of those by their respective degrees of freedom to get SSM and SST. SSM = MSM*DF (numerator degrees of freedom). SST = MST*(DF + DFDen).

Reinaldo

Brilliant solution, Cameron! Thank you very much! I just would like to understand one point:

In the Fit Model, I added

Subject & Random

Timepoint

Subject * Timepoint & Random

in the Construct Model Effects.

In the Fit Model report, REML Variance Component Estimantes table describes the random effect rows for Subject, Subject * Timepoint and Total. In this way, when you suggest to calculate the MSM, should I choose the MSE (Var Component) of Subject to multiply by F-ratio?

Thank you!