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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. 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. | An example of its use in macro form is given below. Just cut and paste into a SPSS syntax window to use. In the syntax window 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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| [SNIP] * |
[CUT AND PASTE ALL BELOW THIS LINE] |
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| * Dependent Correlation Comparison Program. | * Dependent Correlation Comparison Program. |
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| * Compares correlation coefficients from the same sample. | * Compares correlation coefficients from the same sample. |
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| * See Cohen & Cohen (1983), p. 57. | * See Cohen & Cohen (1983), p. 57. |
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| * Sam Field, sfield@mail.la.utexas.edu , March 1, 2000. ******** this input is inputted in the macro call at end of this syntax********* |
* 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. ***************macro and macro call************** **** tests if rxy=rvy and outputs a t-statistic plus one and two-tailed p-values |
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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| COMPUTE #tden = sqrt(2*((!n-1)/(!n-3))*#detR + ((#rbar**2) * ((1-!rxv)**3))). | COMPUTE #tnum = (#diffr) * (sqrt((!n-1)*(1 + !rxv))). |
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| COMPUTE t= (#tnum/#tden). COMPUTE df = !n - 3. | COMPUTE #tden = sqrt(2*((!n-1)/(!n-3))*#detR + ((#rbar**2) * ((1-!rxv)**3))). |
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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 t= (#tnum/#tden). |
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| LIST t df p_1_tail p_2_tail. | COMPUTE df = !n - 3. COMPUTE p_1_tail = 1 - CDF.T(abs(t),df). COMPUTE p_2_tail = (1 - CDF.T(abs(t),df))*2. LIST t df p_1_tail p_2_tail. |
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 in macro form is given below. Just cut and paste into a SPSS syntax window to use. In the syntax window 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.
* 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.
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).
COMPUTE #rbar = (!rxy + !rvy)/2.
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.
COMPUTE p_1_tail = 1 - CDF.T(abs(t),df).
COMPUTE p_2_tail = (1 - CDF.T(abs(t),df))*2.
LIST t df p_1_tail p_2_tail.
exe.
!enddefine.
*********************
williams rxy=r12 rvy=r13 rxv=r23 n=nsize.