[Rasch] Differences in alpha for Winsteps and R

William Fisher william at livingcapitalmetrics.com
Wed Jul 12 07:27:27 AEST 2017

See Linacre (1996). See section 19.83 in the Winsteps manual, where this statement appears:

"In general, Test Reliability reported by Classical Test Theory (Cronbach Alpha, KR-20) is higher than Rasch Reliability."

This happens in part because the true variance component of CTT reliability is estimated as a correlational function, whereas Rasch separation reliabilities estimate true variance by subtracting the mean square error variance from the total variance. When an instrument is off-target and uncertainty is inflated, Rasch separation reliability may be lower than Cronbach's alpha.

For more info on the original conception, see Andrich (1982); see equation 17 for a contrast of Andrich's and Wright's separation indexes. Also see Wright and Masters (1982, pp. 92, 105-106, 111-113).

Andrich, D. (1982, June). An index of person separation in Latent Trait Theory, the traditional KR-20 index, and the Guttman scale response pattern. Education Research and Perspectives, 9(1), 95-104 [http://www.rasch.org/erp7.htm].

Linacre, J. M. (1996). True-score reliability or Rasch statistical validity? Rasch Measurement Transactions, 9(4), 455 [http://www.rasch.org/rmt/rmt94a.htm].

Wright, B. D., & Masters, G. N. (1982). Rating scale analysis: Rasch measurement. Chicago, Illinois: MESA Press.

> On July 11, 2017 at 11:00 AM Stuart Luppescu <lupp at uchicago.edu> wrote:
> Hello fellow Raschies, I'm writing reports on a number of assessments,
> including Rasch and non-Rasch statistics. It's easier to calculate the
> Cronbach's alpha using the psych package in R than to read it from the
> Winsteps output so that's what I'm using for that. But I've noticed
> that what psych::alpha() calculates is rather different from what
> appears in Table 3 in Winsteps. For example, for 1 assessment, Winsteps
> reports (for all forms together):
> due to missing data)
> but psych::alpha() gives 0.55 or 0.68 (depending on the form)
> Anyone know why there should be such a difference?
> -- 
> Stuart Luppescu
> Chief Psychometrician (ret.)
> UChicago Consortium on School Research
> http://consortium.uchicago.edu
> lupp at uchicago.edu
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