My personal idea is that in the field of MANOVA or ANOVA analysis, SPSS software is very accurate and reliable.

I have written Two-way MANOVA syntax for an example of analysis.

GLM Percent Score BY Cycle Age

/METHOD=SSTYPE(3)

/INTERCEPT=INCLUDE

/POSTHOC=Cycle Age(DUNCAN LSD)

/PLOT=PROFILE(Cycle Age Cycle*Age) TYPE=LINE ERRORBAR=NO MEANREFERENCE=NO YAXIS=AUTO

/EMMEANS=TABLES(Cycle) COMPARE ADJ(LSD)

/EMMEANS=TABLES(Age) COMPARE ADJ(LSD)

/EMMEANS=TABLES(Cycle*Age) COMPARE (Age) ADJ(LSD)

/PRINT=DESCRIPTIVE ETASQ OPOWER HOMOGENEITY

/CRITERIA=ALPHA(.05)

/DESIGN= Cycle Age Cycle*Age.

Abolfazl Ghoodjani Thank you for you response. I am just wondering where the difference lies exactly so that I could fix the R output.

My guess is that SPSS does not calculate the partial eta square but just the eta square

Maybe also:

https://stats.stackexchange.com/questions/240751/why-is-pillais-trace-equal-to-partial-eta-squared-in-a-repeated-measures-manova

In attachment an R script for the eta square and partial eta squares

Dear Jos Feys , Regards

SPSS software reports partial eta square in all its (General) Linear Model analysis.

Abolfazl Ghoodjani I think what Jos Feys is trying to say is that there has been some discussion in the literature about SPSS's output of the eta squared while labeling it as partial eta squared. I am not sure if the newer version of SPSS has corrected that labeling issue or not. Overall, Jos Feys is right. One of the main issues is with the different eta square between R and SPSS.

Personally, I am more familiar with the way R allows to calculate eta square, partial eta square and generalized eta square. When there are repeated measures involved, Bakeman (2005) has recommended to use the generalized eta square. Using the 'ez' R package, this is quite easy. With SPSS one has to manually calculate this effect size statistic.

Bakeman, R. Recommended effect size statistics for repeated measures designs. Behavior Research Mehtods, 2005, 37, 379-384

As to the SPSS partial eta square issue, see:

Article Eta Squared, Partial Eta Squared, and Misreporting of Effect...

When diciding which effect size to use one should of course follow the recommendations of the Journals one intends to submit a report.

Let me make two personal comments.

You also may look at the effectsize package (https://easystats.github.io/effectsize/), which offers a large variety of effect size for a large variety of models. There is also a vignette (https://easystats.github.io/effectsize/articles/anovaES.html) that might be interesting for you.