Post-hoc Power, effect size for Chi-square

I need help with my post-hoc power analysis, specifically the effect size:

I measure children's successrate under four conditions.
My dependent variable is nominal (specifically binary, with the values 0 (failed) and 1(succeeded))
My independent variable is nominal with four categories.
My data looks like this:
  • Condition 1: N = 42; 9 succeeded
  • Condition 2: N = 43; 4 succeeded
  • Condition 3: N = 31; 3 succeeded
  • Condition 4: N = 15; 4 succeeded
I did a Fisher's exact/ Chi square test with SPSS and now I'd like to calculate the power with G*Power 3, for which I need w, the effect size.

According to a book, w is calculated the same way as the normal Chi-square if one substitutes the frequencies of the events/expected events with their relative frequencies. I double-checked my calculations and my w should be approx. 0.4425, which to me seems kind of high, given that my Fisher's exact Test value is 4.599, and my two-tailed significance 0.191.
Also, according to german wikipedia, w and Cramer's V are equivalent in such tests, and SPSS gives me a Cramer's V of 0.189.

I'd be very grateful If somebody could help me understand why my value for w differ's from SPSS' Cramer's V and, if both are incorrect, point me to how I can calculate the necessary values for my Power analysis.

I'm also uncertain how to account for my unbalanced design in the power analysis.


A Schaman