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The Analysis of Variance and Covariance Techniques in Relation to the Conventional Formulas for the Standard Error of a Difference

Published online by Cambridge University Press:  01 January 2025

Max D. Engelhart
Max D. Engelhart*
Affiliation:
Department of Examinations, Chicago City Junior Colleges
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Abstract

In this paper it is demonstrated that the analysis of variance techniques yield results equivalent to the calculation of t by means of expressions based on the short or the long formula. It is also shown that the covariance technique gives results equivalent to those obtained by means of the formula for t which should be used with matched groups. The conditions necessary for equivalent results are such that the conventional formulas for t would normally be used rather than the variance or covariance techniques. However, a knowledge of the relationships described in this paper should contribute to one's understanding of the variance and covariance techniques.

Type
Original Paper
Information
Psychometrika , Volume 6 , Issue 4 , August 1941 , pp. 221 - 233
Copyright
Copyright © 1941 The Psychometric Society

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Footnotes

*

The relationships described in this paper were brought to the attention of the author by the excellent article of Eugene Shen (8). The proofs given here and the examples are the work of the present author.

References

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