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Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Tahani Coolen-Maturi

Maturi, T.A. & Elsayigh, A. (2010). A Comparison of Correlation Coefficients via a Three-Step Bootstrap Approach. Journal of Mathematics Research 2(2): 3-10.

Author(s) from Durham

Abstract

In this paper we compare ten correlation coefficients using a three-step bootstrap approach (TSB). A three-step bootstrap
is applied to determine the optimal repetitions, B, to estimate the standard error of the statistic with certain degree of
accuracy. The coefficients in question are Pearson product moment (r), Spearman’s rho (ρ), Kendall’s tau (τ) , Spearman’s
Footrule (Ft), Symmetric Footrule (C), the Greatest deviation (Rg), the Top - Down (rT ), Weighted Kendall’s tau (τw),
Blest (ν), and Symmetric Blest’s coefficient (ν∗). We consider a standard error criterion for our comparisons. However,
since the rank correlation coefficients suffer from the tied problem that results from the bootstrap technique, we use
existing modified formulae for some rank correlation coefficients, otherwise, the randomization tied-treatment is applied.