One-Sample $t$-Test When Sampling from a Mixture of Normal Distributions

Austin F. S. Lee, John Gurland

Type: Article

Publication Date: 1977-07-01

Citations: 22

DOI: https://doi.org/10.1214/aos/1176343904

Abstract

For the one-sample $t$-test a new form of the exact distribution of the test statistic $t^2$ is obtained when sampling from a distribution which is a mixture of two normal distributions. A numerical example is provided to show that the size of the test can differ greatly when sampling from distributions having the same skewness and kurtosis. Contours of equal size are plotted for a particular case in a certain cross section of the parameter space.

Locations

The Annals of Statistics - View - PDF

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+	The effect of skewness and kurtosis on the one-sample<i>T</i>test and the impact of knowledge of the population standard deviation	1993	Wilkie W. Chaffin Steven G. Rhiel
+	On comparing several straight lines under heteroscedasticity and robustness with respect to departure from normality	1982	Wei Tan
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+	On approximating probability distributions of a statistic of brown-forsythe from normal and non-normal universes	1982	Wei Tan
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+ PDF Chat	Managing the Assumption of Normality within the General Linear Model with Small Samples: Guidelines for Researchers Regarding If, When and How.	2023	Conrad Stanisław Zygmont

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+	Sampling distributions from a compound normal parent population	1949	Hannes Hyrenius
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