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enhancing the procedure for estimating alpha Reliability
I just sent an article ms. related to reliability estimation. One of the main (accidental) results is that the procedure used in SPSS (listwise omitting) is misleading and VERY unstable against the missing values. When using the listwise selection, the alpha estimates the reliability of a SPECIFIC type of score formed By (x1+x2+â€¦+xk) which also leaves missing values in the sum. If the SUM or MEAN operation is used in forming the score, this listwise procedure is not proper at all. If the CASEwise omitting would be used and Lord & Novick (1968) formula, the estimate would be much more stable and appropriate for the SUM and MEAN cases.
The problem is that when there are missing values and when using the listwise omitting BUT using SUM or MEAN operation in the summing, the alpha estimate for the reliability in SPSS is not valid AT ALL. By using SUM or MEAN, all the cases get the value and then (if having missing values) the SPSS estimate of reliability is irrelevant and the estimate for the reliability is not only an underestimate (as alpha always is) but a a totally INCORRECT estimate when the dataset includes missing values.
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