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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 . |
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| * Dependent Correlation Comparison Program. | |
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| * Dependent Correlation Comparison Program. | * Compares correlation coefficients from the same sample. |
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| * Compares correlation coefficients from the same sample. | * See Cohen & Cohen (1983), p. 57. |
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| * See Cohen & Cohen (1983), p. 57. | * Sam Field, sfield@mail.la.utexas.edu , March 1, 2000. |
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| * Sam Field, sfield@mail.la.utexas.edu, March 1, 2000. |
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| /r12 r13 r23 nsize. | /r12 r13 r23 nsize. |
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| END DATA. | END DATA. |
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| /rvy = !tokens(1) | /rvy = !tokens(1) |
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| /rxv = !tokens(1) | /rxv = !tokens(1) |
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| /n = !tokens(1)). | /n = !tokens(1)). |
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| COMPUTE #diffr = !rxy - !rvy. | COMPUTE #diffr = !rxy - !rvy. |
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| *Calculate (rxy + rvy)^2 . | *Calculate (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. | * Evaluate the value of the t statistic. |
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| * against a t distribution with n - 3 degrees if freedom for. | * against a t distribution with n - 3 degrees if freedom for. |
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| * statistical significance. | * statistical significance. |
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| COMPUTE p_1_tail = 1 - CDF.T(abs(t),df). COMPUTE p_2_tail = (1 - CDF.T(abs(t),df))*2. |
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. | * Print the results. |
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| LIST t df p_1_tail p_2_tail. |
LIST t df p_1_tail p_2_tail. |
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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.