doubt about realibility analysis

[Rodrigo Briceño-2]

Dear SPSS users. Usually when we work on developing scales, the
attention goes primarily to Alpha-Cronbach (AC) coefficient. One
friend of mine that is working on the subject found an AC of 0.776. In
his analysis he also considered the test of T2 Hotelling (p-value
0.573). As far as I understand this is a multivariate test for
comparison of means of the variables of the scale. In this case the
test implies no rejection of H0, what it means that the variables used
for developing the scale have all statistically equal means.

He asked me if I know what is the relation between the AC and the T2
Hotelling test. In other words: when you got a 0.7 or higher on AC you
should get a lowest p-value (rejection of H0) in T2 Hotelling?

If anybody knows more about this topic I will appreciate your comments.

Thanks

--
Rodrigo Briceño
Economist
[hidden email]
MSN: [hidden email]
SKYPE: rbriceno1087

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[David Marso]

Why should there be *any* relationship?

Alpha and T2 measure completely different things.
It is possible for a sets of measured variables to have
1. identical means and high intercorrelation (W).
2. Disparate means and zero intercorrelation (X).
3. identical means and zero correlation (Y).
4. Disparate means and high intercorrelation (Z).
Very easy to simulate such situations:
In fact there is *NO* such necessary relationship and your friend could perhaps  use a stats review!---
INPUT PROGRAM.
NUMERIC W1 TO W5 X1 TO X5 Y1 TO Y5 Z1 TO Z5 (F8.3).
LOOP #=1 TO 1000.
+  COMPUTE #BASE=NORMAL(1).
+  DO REPEAT W=W1 TO W5 /X=X1 TO X5 / Y=Y1 TO Y5 /Z=Z1 TO Z5/ #=1 TO 5.
+    COMPUTE W=.95 *#BASE + NORMAL(1).
+    COMPUTE X=NORMAL(1)+ #*.5.
+    COMPUTE Y=NORMAL(1).
+    COMPUTE Z=W+X.
+  END REPEAT.
+  END CASE.
END LOOP.
END FILE.
END INPUT PROGRAM.

RELIABILITY
  /VARIABLES=W1 TO W5/SCALE(ALPHA)=ALL/MODEL=ALPHA  /STATISTICS=DESC HOTELLING .
RELIABILITY
  /VARIABLES=X1 TO X5/SCALE(ALPHA)=ALL/MODEL=ALPHA  /STATISTICS=DESC HOTELLING .
RELIABILITY
  /VARIABLES=Y1 TO Y5/SCALE(ALPHA)=ALL/MODEL=ALPHA  /STATISTICS=DESC HOTELLING .
RELIABILITY
  /VARIABLES=Z1 TO Z5/SCALE(ALPHA)=ALL/MODEL=ALPHA  /STATISTICS=DESC HOTELLING .

Rodrigo Briceño-2 wrote

Dear SPSS users. Usually when we work on developing scales, the
attention goes primarily to Alpha-Cronbach (AC) coefficient. One
friend of mine that is working on the subject found an AC of 0.776. In
his analysis he also considered the test of T2 Hotelling (p-value
0.573). As far as I understand this is a multivariate test for
comparison of means of the variables of the scale. In this case the
test implies no rejection of H0, what it means that the variables used
for developing the scale have all statistically equal means.

He asked me if I know what is the relation between the AC and the T2
Hotelling test. In other words: when you got a 0.7 or higher on AC you
should get a lowest p-value (rejection of H0) in T2 Hotelling?

If anybody knows more about this topic I will appreciate your comments.

Thanks

--
Rodrigo Briceño
Economist
[hidden email]
MSN: [hidden email]
SKYPE: rbriceno1087

=====================
To manage your subscription to SPSSX-L, send a message to
[hidden email] (not to SPSSX-L), with no body text except the
command. To leave the list, send the command
SIGNOFF SPSSX-L
For a list of commands to manage subscriptions, send the command
INFO REFCARD