A variable in common (overlap) e.g. of form r(W,X) = r(W,Z).

A test for this comparison goes under various names the Williams test, Williams-Hotelling or Hotelling test.

• This can be implemented using SPSS syntax provided at http://www.utexas.edu/its/rc/answers/general/gen28.html .

An example of its use together with syntax is given below. Just cut and paste into a SPSS syntax window to use. You can also use the Williams-Hotelling test by typing equalcor at a UNIX prompt on a CBU machine.

* Dependent Correlation Comparison Program. * Compares correlation coefficients from the same sample. * See Cohen & Cohen (1983), p. 57. * Sam Field, sfield@mail.la.utexas.edu, March 1, 2000.

******** this input is inputted in the macro call at end of this syntax********* * Three pairs of correlations to compare*****

set format f10.5. DATA LIST free /r12 r13 r23 nsize. BEGIN DATA .50 .32 .65 50 .59 .31 .71 30 .80 .72 .89 26 END DATA.

***************macro and macro call************** **** tests if rxy=rvy and outputs a t-statistic plus one and two-tailed p-values

define williams (rxy = !tokens(1)

• /rvy = !tokens(1) /rxv = !tokens(1) /n = !tokens(1)).

COMPUTE #diffr = !rxy - !rvy.

COMPUTE #detR = (1 - !rxy **2 - !rvy**2 - !rxv**2)+ (2*!rxy*!rxv*!rvy). *Calculate (rxy + rvy)^2 . COMPUTE #rbar = (!rxy + !rvy)/2.

* Calculate numerator of t statistic. COMPUTE #tnum = (#diffr) * (sqrt((!n-1)*(1 + !rxv))).

COMPUTE #tden = sqrt(2*((!n-1)/(!n-3))*#detR + ((#rbar**2) * ((1-!rxv)**3))).

COMPUTE t= (#tnum/#tden). COMPUTE df = !n - 3.

* Evaluate the value of the t statistic. * against a t distribution with n - 3 degrees if freedom for. * statistical significance. COMPUTE p_1_tail = 1 - CDF.T(abs(t),df). COMPUTE p_2_tail = (1 - CDF.T(abs(t),df))*2.

* Print the results. LIST t df p_1_tail p_2_tail. exe. !enddefine.

*********************

williams rxy=r12 rvy=r13 rxv=r23 n=nsize.