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| A variable in common (overlap) e.g. of form r(W,X) = r(W,Z). | A variable in common (overlap) e.g. of form r(W,X) = r(W,Z). |
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| A test for this comparison goes under various names the Williams test, Williams-Hotelling or Hotelling test. | A test for this comparison goes under various names the Williams test, Williams-Hotelling or Hotelling test. |
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| This can be implemented using SPSS syntax provided at http://www.utexas.edu/its/rc/answers/general/gen28.html . | . 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. In the syntax choose select all and click the run arrow. Edit the data in the spreadsheet as required. You can also use the Williams-Hotelling test by typing '''equalcor''' at a UNIX prompt on a CBU machine. |
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| 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. |
[CUT AND PASTE ALL BELOW THIS LINE] |
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| ******** this input is inputted in the macro call at end of this syntax********* | ************ this input is inputted in the macro call at end of this syntax********* |
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| 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. |
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. |
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| ***************macro and macro call************** **** tests if rxy=rvy and outputs a t-statistic plus one and two-tailed p-values |
***************macro and macro call************** **** tests if rxy=rvy and outputs a t-statistic plus one and two-tailed p-values |
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| define williams (rxy = !tokens(1) | define williams (rxy = !tokens(1) |
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| COMPUTE #diffr = !rxy - !rvy. | COMPUTE #diffr = !rxy - !rvy. |
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| COMPUTE #detR = (1 - !rxy **2 - !rvy**2 - !rxv**2)+ (2*!rxy*!rxv*!rvy). *Calculate (rxy + rvy)^2 . COMPUTE #rbar = (!rxy + !rvy)/2. |
COMPUTE #detR = (1 - !rxy **2 - !rvy**2 - !rxv**2)+ (2*!rxy*!rxv*!rvy). *Calculate (rxy + rvy)^2 . COMPUTE #rbar = (!rxy + !rvy)/2. |
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| * Calculate numerator of t statistic. COMPUTE #tnum = (#diffr) * (sqrt((!n-1)*(1 + !rxv))). |
* Calculate numerator of t statistic. COMPUTE #tnum = (#diffr) * (sqrt((!n-1)*(1 + !rxv))). |
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| COMPUTE #tden = sqrt(2*((!n-1)/(!n-3))*#detR + ((#rbar**2) * ((1-!rxv)**3))). | COMPUTE #tden = sqrt(2*((!n-1)/(!n-3))*#detR + ((#rbar**2) * ((1-!rxv)**3))). |
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| COMPUTE t= (#tnum/#tden). COMPUTE df = !n - 3. |
COMPUTE t= (#tnum/#tden). COMPUTE df = !n - 3. |
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| * 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. |
* 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. |
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| * Print the results. LIST t df p_1_tail p_2_tail. exe. !enddefine. |
* Print the results. LIST t df p_1_tail p_2_tail. exe. !enddefine. |
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| ********************* | ********************* |
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| williams rxy=r12 rvy=r13 rxv=r23 n=nsize. | williams rxy=r12 rvy=r13 rxv=r23 n=nsize. |
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. In the syntax choose select all and click the run arrow. Edit the data in the spreadsheet as required. You can also use the Williams-Hotelling test by typing equalcor at a UNIX prompt on a CBU machine.
[CUT AND PASTE ALL BELOW THIS LINE]
* 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.
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williams rxy=r12 rvy=r13 rxv=r23 n=nsize.