Does anybody know of a correct way to calculate the optimal sample size for a discriminant analysis? I did neither find info on that, nor an R package or a webtool.
As a makeshift solution, I employed the MANOVA function from G*Power (because Tabachnick and Fidell describe discriminant analysis as "MANOVA turned around"). In the "MANOVA: Global effects", I entered my number of groups in the "Number of groups" form field, and the number of my discriminant variables in the "Response variables" form field.
However, when I select "MANOVA: Special effects and interactions", in addition to the "Response variables" form field, I also have to input the "Number of predictors", and I don't know what to enter there (see attachment).
Is there a better way to calculate the sample size? If not, what do I need to enter in the "Number of predictors" form field?
Thanks in advance for any suggestion!
Discriminant analysis can be thought of as a regression. See Snedecor and Cochran, Statistical Methods, 6th ed. Sect 13.14. Perhaps this and G*power can help. Best, D. Booth
Hello Sir,
In G*Power, select F-tests (test family) MANOVA (Global effects).
You'll need to supply:
1) Effect size (in Cohen's f-squared metric)
2) Alpha level (protection against Type I error)
3) Target power
4) Number of groups (in DA, group membership is the dependent variable)
5) Response variables (number of measures or independent variables that will potentially be used to discriminate among groups).
The internal mechanics of DA and one-way MANOVA are exactly the same: Scores on the measures are combined to optimally separate group centroids in (hyper)space.
Good luck with your work!
David Morse, thank you very much. I already figured that, but it is good to have someone affirm this approach because I have never done a DA power analysis before!
However, my remaining problem is the specification in case of the "special effects and interactions" (see the screenshot). I should have made that more clear, so sorry for the confusion.
In a regression, if I want to make hypotheses about the significance of certain predictors (which I want), I need to select "special effects and interactions". I thought that this should also be possible in a DA when I also chose the "special effects and interactions" of a MANOVA. However, in this case I have to enter something in the field "number of predictors", and I do not know what to input there because I already specified the predictors in "Response variables" and the criterion groups in "Numer of groups".
Special effects would refer to restricted tests; interactions refers to the combinatorial effect of two or more factors (independent variables in MANOVA). Neither seems germane to your question.
"Significance" of individual measures (IVs in DA) will depend on: (a) the magnitude of explanatory power (for group differences); (b) the number of other predictors under analysis (and whether multicollinearity is an issue); (c) the specific discriminant function root being inspected (maximum roots = groups - 1); and (d) sample size.
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