Nonparametric Measure of Linear Trend

Abstract

This paper proposes and develops a nonparametric statistical procedure for estimating linear trend effect on data using nonparametric regression methods based on ranks, assuming one of the sampled populations is a measurement on a time scale. The populations of interest may be measurements on as low as the ordinal scale. The nonparametric regression-based linear trend estimate is shown to be similar in computation to the Spearman’s Rank Correlation Coefficient. Test statistics are developed for testing hypotheses on the linear trend effect. Sample data are used to illustrate the proposed method.

Keywords: Nonparametric, Linear, Test Statistic, Measure, Trend, Ratio