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The Effect of Sequential Dependence on the Sampling Distributions of KR-20, KR-21, and Split-Halves Reliabilities [microform] / Walter L. Sullins
Bib ID 5219691
Format BookBook, MicroformMicroform, OnlineOnline
Author
Sullins, Walter L
 
Online Versions
Description [Washington, D.C.] : Distributed by ERIC Clearinghouse, 1971 
9 p. 
Summary

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)

Notes

ERIC Note: Paper presented at the Annual Meeting of the American Educational Research Association, New York, New York, February 1971.

May also be available online. Address as at 14/8/18: https://eric.ed.gov/

Reproduction Microfiche. [Washington D.C.]: ERIC Clearinghouse microfiches : positive. 
Subjects Comparative Analysis.  |  Correlation.  |  Error of Measurement.  |  Item Analysis.  |  Measurement Techniques.  |  Reliability.  |  Sample Size.  |  Sampling.  |  Statistical Analysis.  |  Test Construction.  |  True Scores.  |  Kuder Richardson Reliability Formulas  |  Monte Carlo Studies
Available From ERIC 
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008 080220s1971    xxu ||| b     ||| | eng d
035 |9(ericd)ED049276
037 |aED049276|bERIC
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091 |amfm
100 1 |aSullins, Walter L.
245 1 4 |aThe Effect of Sequential Dependence on the Sampling Distributions of KR-20, KR-21, and Split-Halves Reliabilities|h[microform] /|cWalter L. Sullins.
260 |a[Washington, D.C.] :|bDistributed by ERIC Clearinghouse,|c1971.
300 |a9 p.
500 |aERIC Note: Paper presented at the Annual Meeting of the American Educational Research Association, New York, New York, February 1971.|5ericd
520 |aFive-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)
530 |aMay also be available online. Address as at 14/8/18:|uhttps://eric.ed.gov/
533 |aMicrofiche.|b[Washington D.C.]:|cERIC Clearinghouse|emicrofiches : positive.
650 1 7 |aComparative Analysis.|2ericd
650 0 7 |aCorrelation.|2ericd
650 1 7 |aError of Measurement.|2ericd
650 0 7 |aItem Analysis.|2ericd
650 0 7 |aMeasurement Techniques.|2ericd
650 1 7 |aReliability.|2ericd
650 0 7 |aSample Size.|2ericd
650 0 7 |aSampling.|2ericd
650 1 7 |aStatistical Analysis.|2ericd
650 1 7 |aTest Construction.|2ericd
650 0 7 |aTrue Scores.|2ericd
653 1 |aKuder Richardson Reliability Formulas
653 0 |aMonte Carlo Studies
856 4 1 |uhttps://eric.ed.gov/?id=ED049276
984 |aANL|cmc 2253 ED049276|d77000000056828
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