Estimating Percentiles of Nonnormal Anthropometric Populations Final Report

Abstract

The most commonly used method for estimating percentiles of anthropometric populations is based on the assumption that the population is normally distributed. This assumption is approximately true for many such variables, e.g., hip breadth. On the other hand, numerous nonnormally distributed anthropometric populations are known to exist, e.g., grip strength. The question of how to estimate percentiles of nonnormal populations is addressed here.

A nonparametric percentile estimation method, based on the use of a kernel-type probability density function estimator, is presented. A “nonparametric” method is defined as a method that does not make or require any assumption about the statistical distribution of the underlying population. Thus, the method can be applied to any population of anthropometric data, regardless of the normality of the data. The method is simple to use; however, a single nonlinear equation must be numerically solved on a computer by any one of numerous well-documented nonlinear root finding methods.

Two examples are used to illustrate the method. In the first example, selected samples of size 50 of hip breadth data are randomly drawn from a population of size 2420 observations from the 1967 anthropometric survey of U.S. Air Force flying personnel. The proposed method is compared to the standard gaussian method. Since this population was selected as normally distributed, the standard method outperforms the proposed nonparametric method. In the case of grip-strength data, the proposed method yields more accurate estimates, in a mean squared error sense, of the upper percentiles of this population. For anthropometric distributions known to be nonnormal or where normality cannot be assumed, the proposed nonparametric method appears a method for consideration.

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References

Bennett

G. K.

(1970). “A Computer Analysis of Parzen's Density Estimator,” unpublished report prepared at Texas Tech University, Lubbock, Texas.

Clauser

C. E.

Alexander

Kennedy

K. W.

(1967). “USAF Anthropometry of Flying Personnel—1967,” Aerospace Medical Research Laboratory, Wright-Patterson Air Force Base, Ohio.

Parzen

(1962). “On Estimation of a Probability Density Function and its Mode,” Annals of Math. Stat., 33, pp. 1065–76.

Roebuck

J. A.

(1957). “Anthropometry in Aircraft Engineering Design,”. J. Aviation Med., 28, pp. 41–56.

Roebuck

J. A.

Kroemer

K. H. E.

Thomson

W. G.

Engineering Anthropometry Methods. New York: Wiley, 1975.

Rosenblatt

(1956). “Remarks on Some Nonparametric Estimates of a Density Function,” Annals of Math. Stat., 26, pp. 832–7.

Wegman

E. J.

(1972a). “Nonparametric Probability Density Estimation: I. A Summary of Available Methods,” Technometrics, 14, pp. 533–46.

Wegman

E. J.

(1972b). “Nonparametric Probability Density Estimation: II. A Comparison of Density Estimation Methods,” Journal of Statistical Computation and Simulation, 1, pp. 225–45.