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

Alan Hutson

Journal of Applied Statistics, 1998, vol. 25, issue 4, 525-533

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.

Date: 1998
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DOI: 10.1080/02664769822990

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