James Lumsden

Variations on a Theme by Thurstone

A test model based on the Thurstone judgmental model is described. By restricting various param eters of the model, 3 Rasch models, 2 pseudo- Rasch models, 3 two-parameter ICC models, and a Webers Law model are derived.

Test Length and Validity

The effect of test length on predictive validity is examined empirically by successively omitting the poorest items and by calculating the correlations between the reduced test scores and the criterion. It was found, for four tests, that the curve of validity against test length had a very gentle slope for the longer tests and that all tests could be reduced by more than 60% without appreciable decreases in validity.

Validity as theoretical equivalence

The validity problem is considered as one of describing the systematic variance of a test in theoretical terms. Using physical examples it is argued that a theoretical description is only possible for a theoretically singular test and that the theory must be sufficiently developed to permit multiple comparisons between theoretical expectations and empirical outcomes. Validation is impossible for individual difference measures based on performance.

Comment on feldt's “use of extreme groups”

Feldt [1] examines the use of the Kelley-Cureton upper and lower 27 per cent rule for the estimation of p. Using a formula for the standard error of rtot developed by Peters and Van Voohris ([3], p. 383), he finds, correctly, that the rule applies exactly only to the case where p is zero. For increasing values of p he finds that the optimal per cent is less than 27 and decreases with p until for p -0.50 no minimum exists. These results, set out in Feldts Table 1, are, on intuitive grounds, incredible. Standard errors which keep on decreasing without limit for smaller and smaller values of q when the cuts implied are themselves subject to sampling error are unbelievable. Any statistical argument which produces such results should be regarded with suspicion. I t turns out that suspicion is justified. The Peters and Van Voohris expression for ar ,