The Effect of Sequential Dependence on the Sampling Distributions of KR-20, KR-21, and Split-Halves Reliabilities.

N

9

Comparative Analysis; Correlation; Error of Measurement; Item Analysis; Measurement Techniques; Reliability; Sample Size; Sampling; Statistical Analysis; Test Construction; True Scores

Five-hundred dichotomously scored response patterns were generated with sequentially independent (SI) items and 500 with dependent (SD) items for each of thirty-six combinations of sampling parameters (i.e., three test lengths, three sample sizes, and four item difficulty distributions). KR-20, KR-21, and Split-Half (S-H) reliabilities were computed for these 36,000 response matrices and cumulative distribution functions, each based on 500 trials, compiled. Comparison of the sampling distributions suggests that there is more similarity between the SI and SD cumulative distribution functions for KR-21 than KR-20, and either of these have more similarity than S-H. For KR-20, KR-21, and S-H, the similarity of sampling distributions under SI and SD varies directly with test length: the longer the test, the more similar the distributions. On the other hand, similarity varies inversely with sample size: the larger the sample, the more dissimilar the distributions. For both SI and SD item sets, the expected value of KR-21 is less than or equal to that of KR-20 which is less than or equal to the expected value of S-H. Also, for both item sets, the standard error of S-H is greater than that of KR-21 which is greater than or equal to the standard error of KR-20. The standard errors of the three reliability estimates vary inversely with sample size and test length, for both SI and SD items. In every case, SD increased the expected value of the estimate and decreased its standard error. (Author/AE)

1971

ED049276