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The Power of Some Tests of Correlation

Published online by Cambridge University Press:  05 September 2017

E. J. Williams
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Abstract

The coefficient of correlation between suitably defined statistics provides a means of testing various parametric hypotheses. The distribution of such coefficients, when the null hypothesis is not true, takes various forms in different applications. In particular, the correlation coefficients used to test hypotheses about the structural parameters in linear functional relations have doubly non-central distributions.

For tests of correlation in some typical situations, the curvature of the function defining the power in terms of the parameter in the neighbourhood of the null hypothesis is determined. This curvature is shown to be simply related to that of the function defining the squared correlation coefficient in terms of the parameter, in the neighbourhood of its minimum.

Type
Part III — Statistical Theory
Information
Journal of Applied Probability , Volume 12 , Issue S1 , 1975 , pp. 105 - 116
Copyright
Copyright © 1975 Applied Probability Trust 

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References

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