It is not entirely clear, nor I have not found a place in which the information was collected into a single thread, so I decided what to pay attention to this problem here.

Various forms of calculations eta-squared (not partial eta-squared which SPSS gives in outputs!) need generally calculate the sum of the squares or used them with SPSS output. Unfortunately, rarely noticeable it is that the sum of squares in different versions of SPSS GLM (UNIANOVA, MANOVA, GLM) do not add up in the output window for a simple reason. Example SPSS output:

enter image description here

Of course, we are interested in the calculation of the eta "corrected total", ie without the constant value, but as you can see it does not add up to the same value as SPSS output gives us as a total sum of squares.

The reason is the unbalanced factorial plan, that is a different number of observations in the subgroups.


[also in: my sums of squares do not add up! David P. Nichols from 1994 article]

On the one hand this happens, of course, in research tests commonly, on the other hand, some argue that such an approach violates the principles of analysis, still others suggest checking equinumerosity groups chi-square test, which will be insensitive to one-observation difference in subgroups...

If our plan is not "balanced" then to calculate the eta-squared we should use calculated "by hand" instead of the sum of the squares provided by SPSS, because it is for them to count the force effect.

You can also get around this problem using formula that not need the sum of the squares, but only the value of F and df.

Calculating eta squared from F and df

Do you think that this is the correct approach? I look forward to comments and discussion.


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