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Extending Generalized Symmetric Means to Arbitrary Matrix Sampling Designs

Published online by Cambridge University Press:  01 January 2025

Roger Wellington
Roger Wellington*
Affiliation:
Applied Technology Center for Education
*
Requests for reprints should be sent to Roger Wellington, Applied Technology Center for Education, 501 N. Brookhurst St. Suite #316, Anaheim, California 92801.
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Abstract

Generalized symmetric means are redefined in a way which allows them to be calculated for any matrix sampling design. It is proved that these sample gsm's are unbiased estimates of the analogous population gsm's. Illustrative examples are given.

Keywords

item samplingbisamplingbipolykays
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 3 , September 1976 , pp. 375 - 384
Copyright
Copyright © 1976 The Psychometric Society

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Footnotes

This paper is based on Applied Technology Center for Education Technical Memorandum 75-03-01. Special appreciation is expressed to Ken Sirotnik and Tom Knapp for their suggestions on clarifing this presentation.

References

References Notes

Hooke, R. The estimation of polykays in the analysis of variance, 1954, Princeton University: Statistical Research Group.Google Scholar
Knapp, T.Item-examinee sampling. Unpublished manuscript, University of Rochester, 1973.Google Scholar
Pandey, T. N. &Shoemaker, D. M. Estimating moments of universe scores and associated standard errors in multiple matrix sampling for all item-scoring procedures, 1973, Los Alamitos, California: Southwest Regional Laboratory.Google Scholar

References

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