TEST EQUATING FROM BIASED SAMPLES, WITH APPLICATION TO THE ARMED SERVICES VOCATIONAL APTITUDE BATTERY

The problem of equating a new standardized test to an old reference te st is considered when the samples for equating are not randomly select ed from the target population of test takers. Two problems with equati ng from biased samples are distinguished: (a) bias in the equating fun ction arising from nonrandom selection of the equating sample, and (b) excessive variance in the equating function at scores that are relati vely underrepresented in the equating sample relative to the target po pulation. A theorem is presented that suggests that bias may not be a major problem for equating, even when the marginal distributions of sc ores are distorted by selection. Empirical analysis of data for equati ng the Armed Services Vocational Aptitude Battery (ASVAB) based on sam ples of recruits and applicants supports this contention. Analysis of ASVAB data also indicates that excessive variance in the equating func tion is a more serious issue. Variance-reducing methods, which smooth the test score distributions using extended beta binomial and loglinea r polynomial models before equating by the equipercentile method, are presented. Empirical evidence suggests that these smoothing models are successful and yield equating functions that improve on both equiperc entile and linear equating of the raw scores.