- Posts: 75
The T-score table was computed using the summed score Lord-Wingersky recursive algorithm (Lord & Wingersky, 1984), extended to polytomous items (Thissen, Pommerich, Billeaud, & Williams, 1995). The algorithm is well-validated and has become the basis for several important innovations in educational and psychological testing (Cai, 2015). For each summed score, the algorithm computes the most likely EAP-based theta (T-score) estimate, along with the most likely standard error. It therefore represents a type of average across all the possible response patterns that might produce a single summed score. It is certainly possible that individual patterns would produce higher or lower thetas along with a slightly larger SE. But deviations from the most probable patterns are unlikely, and these differences will be cancelled out in group-level analyses. These tables are not to be used when there is missing data. In cases of missing data, using the summed score table would underestimate the error and bias the score estimate away from the mean. As with response pattern scores (e.g., produced by HealthMeasures Scoring Service), the summed score EAP estimates show greater reliability in the middle of the trait, while the errors become larger towards the extremes.
Cai, L. (2015). Lord–Wingersky algorithm version 2.0 for hierarchical item factor models with applications in test scoring, scale alignment, and model fit testing. Psychometrika, 80(2), 535-559.
Lord, F. M., & Wingersky, M. S. (1984). Comparison of IRT true-score and equipercentile observed-score" equatings". Applied Psychological Measurement, 8(4), 453-461.
Thissen, D., Pommerich, M., Billeaud, K., & Williams, V. S. (1995). Item response theory for scores on tests including polytomous items with ordered responses. Applied Psychological Measurement, 19(1), 39-49.