How to calculate Cronbach's alpha using data from a correlation matrix in SAS?

[daltonbc]

I have a correlation matrix, how can I calculate Cronbach's alpha of my factors using SAS? I don't have the original data set, just the correlation matrix, N, mean and std.

I have a correlation matrix like this:

DATA sol (TYPE=CORR);
INPUT _TYPE_ $ _NAME_ $ idealism relativism misanthropy gender attitude;
CARDS;
N        .        153     153     153     153      153
mean     .        3.64926 3.35810 2.32157 1.18954 2.37276
std      .        0.53439 0.57596 0.67560 0.39323 0.52979
corr idealism     1.0000   .       .       .       .
corr relativism  -0.0870  1.0000   .       .       .
corr misanthropy -0.1395  0.0525  1.0000   .       .
corr gender      -0.1011  0.0731  0.1504  1.0000   . 
corr attitude     0.0501  0.1581  0.2259 -0.1158  1.0000
;
proc factor;
    var  idealism relativism misanthropy gender attitude;
run;

I was able to perform factorial analysis with my correlation matrix.

[Reeza]

If I'm reading this correctly, it's the following, for at least the standardized Cronbach Alpha. I don't think you can calculate the non-standardized without full information. 

The standardized Cronbach's alpha can be defined as

where is as above and the mean of the non-redundant correlation coefficients (i.e., the mean of an upper triangular, or lower triangular, correlation matrix).

You have K, the number of elements and the r's to calculate the mean, so proc means, a data step or SQL should get you there though it is somewhat of a manual calculation. 

https://en.wikipedia.org/wiki/Cronbach's_alpha

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@daltonbc wrote:

I have a correlation matrix, how can I calculate Cronbach's alpha of my factors using SAS? I don't have the original data set, just the correlation matrix, N, mean and std.

I have a correlation matrix like this:

DATA sol (TYPE=CORR);
INPUT _TYPE_ $ _NAME_ $ idealism relativism misanthropy gender attitude;
CARDS;
N        .        153     153     153     153      153
mean     .        3.64926 3.35810 2.32157 1.18954 2.37276
std      .        0.53439 0.57596 0.67560 0.39323 0.52979
corr idealism     1.0000   .       .       .       .
corr relativism  -0.0870  1.0000   .       .       .
corr misanthropy -0.1395  0.0525  1.0000   .       .
corr gender      -0.1011  0.0731  0.1504  1.0000   . 
corr attitude     0.0501  0.1581  0.2259 -0.1158  1.0000
;
proc factor;
    var  idealism relativism misanthropy gender attitude;
run;

I was able to perform factorial analysis with my correlation matrix.

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