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help for ^cortesti^
by Herve M. CACI, October 2000
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Test of equality of two correlation coefficients
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     ^cortesti^ #corr1 #n1 #corr2 #n2
     ^cortesti^ #rxy #rxv #rvy #n

Description
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In standard tests for correlation, a correlation coefficient is tested
tested against the hypothesis of no correlation, i.e. R=0. However it is
possible to test whether the correlation coefficient is equal to or
different from another fixed value.
There are situations where you would like to know whether a certain
correlation strength is really different from another one.

In the first form, ^cortesti^ compares two coefficients computed from
two different samples (n1 and n2 are the respective sizes of the samples).
This test is only an approximation, and should only be used when both
samples are larger than 10.

In the second form, ^cortesti^ compares two coefficients Ñ i.e. r(x,y)
and r(v,y) Ñ computed in a single sample using a third coefficient, r(x,v).
The sample size is the fourth argument.

Examples
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. ^cortesti^ .84 63 .75 42

Test of equality of two correlation coefficients
drawn from the two different samples
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Coefficient 1 = 0.840 (n1 =     63)
Coefficient 2 = 0.750 (n2 =     42)

Ho: coefficient 1 = coefficient 2
         z =   1.207
Prob > |z| =   0.2275


. ^cortesti^ .45 .35 .65 200

Comparison of correlation coefficients
drawn from the same sample (n =    200 obs)
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Coefficient r(x,y) = 0.450
Coefficient r(x,v) = 0.350
Coefficient r(v,y) = 0.650

t =  -3.162 (df=   197)

Ha: r(x,y) < r(v,y) --- P < t = 0.001
Ha: r(x,y) = r(v,y) --- P = t = 0.002
Ha: r(x,y) > r(v,y) --- P > t = 0.999

Also see
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Book:  Cohen J. & Cohen P. (1983) "Applied Multiple Regression/Correlation
       Analysis for the Behavioral Sciences". Hillsdale, NJ: Lawrence
       Erlbaum Associates (2nd Ed).