# GPOWER-based sample size determination

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• #3840

Hello all, pardon me for the rather longer than usual posting but I want to use Power analysis to determine my sample size for 3 distinct cases and struggling quite a bit.

Specifically, I want to apply the GPower tool (v 3.1.2) available free from here:

It is clear that GPower can determine sample size N for Linear Regression and ANOVA and MANOVA for example. I want to use it in an “a priori sample size determination mode given the 4 required inputs: alpha, Power = 1-beta, Effect Size (ES) and number of variables”. So this is all great stuff but I am toying quite a bit using GPower to address each of these 3 research cases:

Case 1: I am using (Exploratory) Factor Analysis and this is not supported in GPower at all as this is not Regression or ANOVA or a t-test or an F-test type of application.  The question is thus “Can we use GPowerr here for FA? If so, what settings do I need to use?”

Case 2: I am using CATREG. GPower does not offer this choice but instead offers “Linear multiple regression: Fixed Model, R^2 deviation from zero”. So I was thinking to apply this using a middle of the road Effect size of say f^2 = 0.15 for medium as suggested by Cohen and enter the other variables including number of predictors (X’s) to get N. I am somewhat unsure here because I have 3 categorical variables out of say 6 total variables in the model, is this going to work? Do I apply some rule of thumb to inflate the GPower sample size by say 20% for each discrete variable?

Case 3: I am using Multinomial Logistic Regression which says it is supported in GPower but I believe this is only for the Bivariate case as in Y = a+bX where Y (or X?) is categorical. Unfortunately I cannot understand what it is is that GPower is doing here, there are no examples and documentations for me to read in terms of feeding it the right inputs 😉 So this “Logistic regression” in GPower appears to be for the Bivariate case and we have an MLR case. Can we use “Linear multiple regression” instead? If indeed GPower’s Logistic Regression is indeed referring to MLR, then what settings for GPower do we use.

If am on the wrong track here and I cannot determine sample size a priori using GPower, what other paper would you then recommend for EACH of the above 3 cases to look at for sample size determination? The “SampleSizeDetermination.pdf” paper by Bartlett posted elsewhere in this forum is NOT going to work for each of these 3 cases. I want my sample size to be based on Power analysis.

Thank you.

Christos Makrigeorgis, Ph.D.

#3847
diana k
Participant

i have a problem also. Survival

My model has B = 30, se(B) = 9.8, wald chi-squ= =9.7, p = .0019, N= 46

I need to estimate what N is needed for power 0.8 to detect an increase in B of 8.

How do I find this N using g*

Best

Diana

#3846
Jeremy Miles
Participant

Hi Christos

1.  Exploratory factor analysis does not test a null hypothesis, so you can’t do a power analysis.

2.  I’m not familiar with catreg, so I can’t help.

3. For multinomial logistic regression, there are multiple hypotheses to test, so it all gets rather tricky.  When I’m forced to power such a thing, I say that I’m going to investigate the power to distinguish between two of the categories, and then power for a logistic regression.  Power is therefore (probably) underestimated.

Remember that power analysis, according to the ‘Devil’s dictionary of statistics’ is “Guess, disguised as mathematics”.

#3845
Jeremy Miles
Participant

What was your sample size?  I’m not sure I understand the question.

Your result is 30, so where would the 8 come from.

Surviival analysis is hard to power, because of the censoring problem – you need to provide an estimate of censoring, although I think it’s done in some packages.

#3844

I’m absolutely agree with Christos:

Yo cannot do a power analysis for FA because it has not a chance to test null hypothesis.

#3843

Thanks Jeremy and Pablo. On 1. FA, for some reason I had the wrong impression that the “H0: k=3 factors are required” would be an example of an H0, scree analysis usage etc… I guess I better review that.

THank you.

Christos

#3842
Jeremy Miles
Participant

If you want to test such a null hypothesis, you can using confirmatory factor analysis, but power anlaysis is not easy for these models.  Here’s a paper that might help:  http://www.statmodel.com/download/FinalSEMsingle.pdf

J

#3841

THanks Jeremy. Yes, CFA would be needed to confirm my factors but all I have is Likert Survey items to form the factors to begin with, so EFA is needed here. Anyway, there should be an easier solution to running a monte carlo simulation just to get sample size. Let me do some more research, it sure is not an easy question. I may have to use some heuristic rules afterall and just forget power analysis here (either a priori or a posteriori)…

Christos

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