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Direct estimation of the percentile 'p-value' for the one-sample median test

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  • Alan Hutson

Abstract

In this paper we outline and illustrate an easy-to-use inference procedure for directly calculating the approximate bootstrap percentile-type p-value for the one-sample median test, i.e. we calculate the bootstrap p -value without resampling, by using a fractional order statistics based approach. The method parallels earlier work on fractionalorder-statistics-based non-parametric bootstrap percentile-type confidence intervals for quantiles. Monte Carlo simulation studies are performed, which illustrate that the fractional-order-statistics-based approach to the one-sample median test has accurate type I error control for small samples over a wide range of distributions; is easy to calculate; and is preferable to the sign test in terms of type I error control and power. Furthermore, the fractional-order-statistics-based median test is easily generalized to testing that any quantile has some hypothesized value; for example, tests for the upper or lower quartile may be performed using the same framework.

Suggested Citation

  • Alan Hutson, 1998. "Direct estimation of the percentile 'p-value' for the one-sample median test," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(4), pages 525-533.
    • Handle: RePEc:taf:japsta:v:25:y:1998:i:4:p:525-533
    DOI: 10.1080/02664769822990
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    1. Mudholkar, Govind S. & Hutson, Alan D., 1997. "Some refinements of the quasi-quantiles," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 67-74, February.
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    1. Alan Hutson, 1999. "Calculating nonparametric confidence intervals for quantiles using fractional order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(3), pages 343-353.

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