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help for ^cortesti^
by Herve M. CACI, October 2000
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Test of equality of two correlation coefficients ------------------------------------------------

^cortesti^ #corr1 #n1 #corr2 #n2 ^cortesti^ #rxy #rxv #rvy #n

Description -----------

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 i.e. r(x,y) and r(v,y) computed in a single sample using a third coefficient, r(x,v). The sample size is the fourth argument.

Examples --------

. ^cortesti^ .84 63 .75 42

Test of equality of two correlation coefficients drawn from the two different samples ------------------------------------------------

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) -------------------------------------------

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 --------

Book: Cohen J. & Cohen P. (1983) "Applied Multiple Regression/Correlation Analysis for the Behavioral Sciences". Hillsdale, NJ: Lawrence