Question: I was taught that all raw scores on a test have the same raw score standard error, SEM, and this is:
SEM = raw score S.D. * sqrt (1-Reliability).
Why do standard errors for person measures differ?
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Answer: The raw score "test" reliability is based on an average raw score standard error for the sample. But each raw score has a different standard error. The raw score standard errors are biggest at the center of the test and smallest at the extremes. In contrast, the standard error of a Rasch measure is smallest in the center of the test and biggest at the extremes. The plot is an idealization plot of their relationship for a 30 item dichotomous test. But, like the raw score reliability, the Rasch reliability is also based on the average standard error of the sample.
Standard Errors and Reliabilities: Rasch and Raw Score, Rasch Measurement Transactions, 2007, 20:4 p. 1086
The URL of this page is www.rasch.org/rmt/rmt204f.htm
Website: www.rasch.org/rmt/contents.htm