[Rasch] Differences in alpha for Winsteps and R

Jack Stenner jstenner at lexile.com
Wed Jul 12 10:48:53 AEST 2017

My add is " appropriately lower"!

Sent from my iPhone

> On Jul 11, 2017, at 5:27 PM, William Fisher <william at livingcapitalmetrics.com> wrote:
> 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?
>> TIA
>> --
>> Stuart Luppescu
>> Chief Psychometrician (ret.)
>> UChicago Consortium on School Research
>> http://consortium.uchicago.edu
>> lupp at uchicago.edu
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