I am calculating a required sample size for the Repeated Measures ANOVA (within subject). I came across two different packages and the results are different.

Using “WebPower” package and the following function

wp.rmanova(n = NULL, ng = 1, nm = 4, f = 0.25, nscor = 1, alpha = 0.05, power = 0.8, type = 1)

I obtained this result:

Repeated-measures ANOVA analysis

           n    f ng nm nscor alpha power
    175.7464 0.25  1  4     1  0.05   0.8

NOTE: Power analysis for within-effect test
URL: http://psychstat.org/rmanova

Using “pwrss” package and the following function

pwrss.f.rmanova(eta2 = 0.06,  n.levels = 1, n.rm = 4, power = 0.80, alpha = 0.05, corr.rm = 0.50, 
type = "within")

I obtained this result:

 One-way Repeated Measures 
 Analysis of Variance (F test) 
 H0: eta2 = 0 (or f2 = 0) 
 HA: eta2 > 0 (or f2 > 0) 
 ------------------------------ 
 Number of levels (groups) = 1 
 Number of repeated measurements = 4 
 ------------------------------ 
  Statistical power = 0.8 
  Total n = 23 
 ------------------------------ 
 Type of the effect = “within” 
 Numerator degrees of freedom = 3 
 Denominator degrees of freedom = 65.029 
 Non-centrality parameter = 11.579 
 Type I error rate = 0.05 
 Type II error rate = 0.2 

I also used GPower to compare the results and I also obtained different sample sizes based on different effect size specification. When I used the default GPower3 effect size specification I obtained n = 24.

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Using the Cohen’s effect size specification I obtained n = 176.

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There was also an “SPSS” option which gave me a sample size of 61. I also read that if you take Cohen’s calculation a divide the n by number of measurements – 1 and add the number of groups you’ll get to the SPSS sample size calculation which agrees: 176/(4-1) + 1 = 60. Can anyone please advise which approach is correct? The difference in these calculations is massive ranging from 24 to 176.