A sequential triangular test of a correlation coefficient’s null-hypothesis: 0<ρ≤ρ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0 < \rho \le \rho _{0}$$\end{document}

A sequential triangular test of the null-hypothesis H0:0<ρ≤ρ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {H}_{0}{:} 0<\rho \le \rho _{0}$$\end{document} is derived, given a two-dimensional vector of normal random variables (x, y). The test is based on an approximate normally distributed test statistic by Fisher’s transformation of the sample correlation coefficient. We show via simulation that for certain requirements of precision (type-I-, type-II-risk, and a practical relevant effect δ=ρ1-ρ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta =\rho _1 -\rho _0$$\end{document}) the average sample size of the sequential triangular test is smaller than the sample size of the pertinent fixed sample size test.