Dear all,
I've been delighted to just notice that Cohen's formulas for
Effect Size 'w' and the associated power have been implemented in
the 'pwr' package (thanks to Stéphane Champely and others)..
There is one aspect, though, that perplexes me. I'm doing some last
minute post hoc analyses, meaning that my sample size (N=3404) has
been long fixed, and I'm interested in assessing the ES and Power
after the fact..
As far as I can deduce from the implementation of the ES.w2 formula or
Cohen's (1992) own article, it seems to me that the probabilities
p(H0) and p(H1) would simply be the expected and observed absolute
frequencies divided by the sample size N, in that the 'true'
probablities are the observed proportions and the null probabilities
the expected ones. If this is correct, then the effect size and the
power statistics can naturally easily be calculated with the 'pwr'
package. However, this entails that the noncentrality parameter
lambda=N*w^2 is equal to the chi-squared statistic X^2.
observed
p h m a
X 119 64 36 37
Y 594 323 776 1455
expected
p h m a
X 53.62162 29.10458 61.06698 112.2068
Y 659.37838 357.89542 750.93302 1379.7932
observed.p
p h m a
X 0.03495887 0.01880141 0.01057579 0.01086957
Y 0.17450059 0.09488837 0.22796710 0.42743831
expected.p
p h m a
X 0.01575253 0.008550112 0.01793977 0.03296322
Y 0.19370693 0.105139664 0.22060312 0.40534465
ES.w2(observed.p)
[1] 0.2406104
ES.w1(expected.p,observed.p)
[1] 0.2406104
pwr.chisq.test(w=ES.w1(expected.p,observed.p),N=3404,sig.level=.05,
df=3)
Chi squared power calculation
w = 0.2406104
N = 3404
df = 3
sig.level = 0.05
power = 1
NOTE: N is the number of observations
lambda <- 3404*ES.w1(observed.p,expected.p)^2
lambda
[1] 240.9289
pchisq(qchisq(p=.05,df=3,lower.tail=F),ncp=lambda,df=3,lower=F)
[1] 1
Have I missed or misunderstood something here altogether? Should the
alternative H0 probabilities be estimated by e.g. some sort of
fitting? Any pointers, suggestions or assistance would be greatly
appreciated.
-Antti Arppe
--
======================================================================
Antti Arppe - Master of Science (Engineering)
Researcher & doctoral student (Linguistics)
E-mail: [EMAIL PROTECTED]
WWW: http://www.ling.helsinki.fi/~aarppe
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