Dear Gregor,
thank you very much for your comments.
Due to possibly existing general interest I post this message also in
sci.stat.edu.
"Gregor Socan" [EMAIL PROTECTED] wrote
You obviously should not use coefficient alpha. First, if an exclusion of
some people causes such a change, then alpha is too instable to be
interpreted (and your sample is extremely small indeed).
The sample size is indeed a problem. But not only with respect to the
calculation of coefficient alpha: ANY reliability estimate will
potentially suffer from this lack of N.
Maybe the
fenomenon is very stable within persons, but obviously not so much
among persons.
I'm intersted firstly in the variance accounted for by the true score of
an 'underlying construct' and secondly in its temporal stability. So the
calculation of cronbach's alpha (or its variants) seems to be clearly
indicated.
Second, negative correlations are indicators of very serious violations of
assumptions on which alpha is based.
I cannot see that some negative correlations among items violate any
assumptions of the calculation of alpha. These negative correlations are
due to error of measurement and/or sampling. Thus, they represent some
amount of variance which cannot be accounted for by true score variance.
If it were an assumtion of alpha that present error rules out the
calculation of alpha, we would never obtain alphas lower than 1. But of
course I acknolewdge the problem that alpha is not interpretable, when
the average interitem correlation drops below zero (thus leading to
negative alpha).
Difference scores are also very
problematic from reliability point of view. Have you read some
psychometric literature like Lord and Novick (1968)?
I cannot see any inherent problem of assessing the reliability of
difference scores. To my mind, it is misleading to deduce some a priori
unreliability of difference scores when the true score theory is applied
as Gullikson (1950) or Lord and Novick (1968) put it. Under the
assupmtions of strict paralell tests (equal means, equal standard
deviations etc.), a reliability estimate of difference scores cannot be
different from zero unless the assumptions of equal means are violated!
Why do we use tests instead of single items? Because, aggregating items
to a test score boosts the true score variance and dampens error
variance (as long as the items are replications of the measured
construct). To my mind I can enhance the true score variance of
difference scores in the same way. The only distinction to the
estimation of 'usual' absolute scores is the need for twice as much
replications of the 'absolute' measures in order to obtain equal hights
of reliability (compared to the 'absolute' constituents of a difference
score). Thus, the above paradox can easily be circumvented. For more
details you might want to refer to:
Wittmann, W. W. (1988). Multivariate reliability theory: Principles of
symmetry and successful validation strategies. In J. R. Nesselroade R.
B. Cattell (Eds.), Handbook of multivariate experimental psychology (2nd
ed., pp. 505-560). New York: Plenum.
Negative
correlations mean that either your measure is worthless or that you are
using a wrong method to assess quality of your measurements.
If you have single measures with only a small portion of true score
variance, I find it not surprising to obtain some negative correlations
by chance.
And I don't see any other method of assessing the reliabilty if I want
to focus on true score variance of an underlying construct.
Please point me to any fallacies or misunderstandings I may have
flaunted.
Nico
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