Test for equality of complicatedly related average correlations
Hi Ralph, I had the same problem you do a few months ago, and realized that the question I had (does time show a different effect for X than Y) was not best modeled as differences between correlations across individuals, but as whether time interacts with condition. I answered this question with
library(nlme) lme(obs ~ cond*time, random=~cond*time|subj)
...where obs is the responses on the X or Y variable, cond is a factor of either X or Y, and subj is your subject variable. This fits a heirarchical linear model to the data. The relationship between X and time is sig. diff. from the relationship between Y and time if the cond:time fixed effect is true. This approach makes better use of your data, because when you correlate the observations, you're effectively "losing" variability (because correlations are doubly standardized) as well as degrees of freedom (you have 9 df within each individual, but each correlation is only one number). --Adam
On Sat, 6 Sep 2008, Ralph79 wrote:
Dear R-Users, I am currently looking for a way to test the equality of two correlations that are related in a very special way. Let me describe the situation with an example. - There are 100 respondents, and there are 2 points in time, t=1 and t=2. - For each of the respondents and at each of the time points, I have information on 10 X-variables and on 10 Y-variables. - Based on this information, I calculate two correlations for each respondent: cor(X[t=1],X[t=2]) and cor(Y[t=1],Y[t=2]), with X and Y being the vectors of the corresponding 10 variables. - Now I get the average correlations over the whole sample using Fishers Z-transformation, i.e. I have mean(cor(X[t=1],X[t=2])) and mean(cor(X[t=1],X[t=2])) and want to know if the mean correlations are significantly different! I haven't found any test that deals with exactly my situation. Therefore, I "simply" apply a paired t-test based on the individual z-correlations. From my point of view this should be ok, because of the z's normality. However, I am unsure if there is a better way to test the hypothesis that I am interested in? I'd be grateful for any comment or hint. Thank you very much, Ralph ----- Ralph Wirth University Erlangen-Nuremberg, Chair of Statistics GfK Group, Department of Methods and Product Development -- View this message in context: http://www.nabble.com/Test-for-equality-of-complicatedly-related-average-correlations-tp19346312p19346312.html Sent from the R help mailing list archive at Nabble.com.
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