Correlation advice

[Humphrey Paulie]

Hi everyone,
  I gave a test to a sample and then split the sample to three ability groups.
  The alpha for the entire sample is 0.81 but for the 3 ability groups the alpha is 0.11, -1.71 and –0.17. The sample has also taken another test. The alpha reliability of this test for the 3 ability groups is 0.84, 0.88 and 0.79 respectively. When I correlate the two tests for each ability group separately I get r= -.001, r=0.45 and r=0.19 respectively. That is for the low ability group there is no correlation for the intermediate ability group there is sort of a strong correlation and for the high ability people again a weak correlation.
  I like this result because this confirms a suspicion. However, since the alphas are weird I fear it might be a statistical artefact.
  What do you think folks? Can I build a hypothesis on this or is it merely a statistical artefact?
  Thanks
  Cheers
  Humphrey



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[Swank, Paul R]

Since Alpha depends upon correlation, breaking the sample into ability groups ames the groups homegeneous on the ability being measured. My suggestion would be to examine the reliability on the total sample and investigate the differential relations using a general linear model with group, one test, and the group by test interaction in realtion to the other test. If the realtion is differential, then the interaction should be significant.

Paul Swank, Ph.D.
Proffessor and Director of Research
Children's Reseach Institute
University of Texas Health Science Center at Houston

________________________________

From: SPSSX(r) Discussion on behalf of Humphrey
Sent: Tue 11/7/2006 11:27 AM
To: [hidden email]
Subject: Correlation advice



Hi everyone,
  I gave a test to a sample and then split the sample to three ability groups.
  The alpha for the entire sample is 0.81 but for the 3 ability groups the alpha is 0.11, -1.71 and -0.17. The sample has also taken another test. The alpha reliability of this test for the 3 ability groups is 0.84, 0.88 and 0.79 respectively. When I correlate the two tests for each ability group separately I get r= -.001, r=0.45 and r=0.19 respectively. That is for the low ability group there is no correlation for the intermediate ability group there is sort of a strong correlation and for the high ability people again a weak correlation.
  I like this result because this confirms a suspicion. However, since the alphas are weird I fear it might be a statistical artefact.
  What do you think folks? Can I build a hypothesis on this or is it merely a statistical artefact?
  Thanks
  Cheers
  Humphrey



---------------------------------
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[statisticsdoc]

Humphrey,

This is a statistical artefact in the sense that the internal consistency of
the scale is responsible for the effects.  When alpha for a scale is close
to zero, then that scores on that scale will not correlate highly with other
scales even when the correlation between the underlying constructs is close
to unity.  The low correlation merely reflects the way that random
measurement error masks the relationship between constructs.

Negative alphas are possible, but I would be very concerned with the value
that you have for the middle ability group. I would suggest checking for
bugs in the scoring program, data entry, etc.

HTH,

Stephen Brand

For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Humphrey
Sent: Tuesday, November 07, 2006 12:28 PM
To: [hidden email]
Subject: Correlation advice


Hi everyone,
  I gave a test to a sample and then split the sample to three ability
groups.
  The alpha for the entire sample is 0.81 but for the 3 ability groups the
alpha is 0.11, -1.71 and –0.17. The sample has also taken another test. The
alpha reliability of this test for the 3 ability groups is 0.84, 0.88 and
0.79 respectively. When I correlate the two tests for each ability group
separately I get r= -.001, r=0.45 and r=0.19 respectively. That is for the
low ability group there is no correlation for the intermediate ability group
there is sort of a strong correlation and for the high ability people again
a weak correlation.
  I like this result because this confirms a suspicion. However, since the
alphas are weird I fear it might be a statistical artefact.
  What do you think folks? Can I build a hypothesis on this or is it merely
a statistical artefact?
  Thanks
  Cheers
  Humphrey



---------------------------------
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[statisticsdoc]

Stephen Brand
www.statisticsdoc.com

Humphrey,

Another issue that needs consideration is this.  Are you splitting the
sample based on the measure that has the odd alphas?  If you are, then by
splitting the sample into three, you will be restricting the range on the
measure, and in so doing may be  encountering attenuation of the correlation
and alpha due to restriction in range.

HTH,

Stephen Brand


For personalized and professional consultation in statistics and research
design, visit
www.statisticsdoc.com


-----Original Message-----
From: SPSSX(r) Discussion [mailto:[hidden email]]On Behalf Of
Humphrey
Sent: Tuesday, November 07, 2006 12:28 PM
To: [hidden email]
Subject: Correlation advice


Hi everyone,
  I gave a test to a sample and then split the sample to three ability
groups.
  The alpha for the entire sample is 0.81 but for the 3 ability groups the
alpha is 0.11, -1.71 and –0.17. The sample has also taken another test. The
alpha reliability of this test for the 3 ability groups is 0.84, 0.88 and
0.79 respectively. When I correlate the two tests for each ability group
separately I get r= -.001, r=0.45 and r=0.19 respectively. That is for the
low ability group there is no correlation for the intermediate ability group
there is sort of a strong correlation and for the high ability people again
a weak correlation.
  I like this result because this confirms a suspicion. However, since the
alphas are weird I fear it might be a statistical artefact.
  What do you think folks? Can I build a hypothesis on this or is it merely
a statistical artefact?
  Thanks
  Cheers
  Humphrey



---------------------------------
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