# [R] Test for equality of complicatedly related average correlations

Ralph79 ralph.statistics at gmx.net
Sun Sep 7 10:40:28 CEST 2008

```Thank you very much, Adam.

I have to get a bit more familiar with the model you propose in order to
understand if it applies to my problem as well.

My question is not really "does time show a different effect" but "which one
of two measures is more reliable": My respondents have completed exactly the
same questionnaire twice (t=1 and t=2). The questionnaire consisted of two
ways of measuring attribute importance, and the "better" method of measuring
these importances is the one that gives the same importances for each
respondent in t=1 and t=2. In other words: I want to examine test-retest
reliability of the two measures. Naturally, if X(t=1,t=2)-correlation is
higher for a specific respondent than the Y(t=1,t=2)-corralation, than for
this respondent the method that yields the X-importances is more reliable.
All I want to do is to see if this holds for the whole sample as well...

Anyway, thank you again, I will think of your approach.

Ralph

>
> 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).
>
>
> 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
>>
>> --
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>> Sent from the R help mailing list archive at Nabble.com.
>>
>> ______________________________________________
>> R-help at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-help
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>
>

-----
Ralph Wirth
University Erlangen-Nuremberg, Chair of Statistics
GfK Group, Department of Methods and Product Development

--
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