TY - JOUR

T1 - How robust is the modified sequential triangular test of a correlation coefficient against non-normality of the basic variables?

AU - Rasch, Dieter

AU - Yanagida, Takuya

PY - 2017/7/3

Y1 - 2017/7/3

N2 - There is a big lack of knowledge as concerns a test of the null hypothesis H0: 0 < ρ ≤ ρ0. Usually a test applies by some z-statistic according to Fisher (1921), which is approximately normally distributed. However, there is no evidence of whether the approximation is actually good enough—that is, it is of interest how the factual distribution of the respective test statistic holds the type-I risk—and which type-II risk results. Because this question cannot be answered theoretically at present, we try a simulation study in order to gain respective knowledge. For this, we even investigate the case of variables that are not (at all) normally distributed. Moreover, we consider variables not normally distributed but test the simple case of the exact t-test of H0: ρ = ρ0. The results show, in particular, that the test tracing back to R. A. Fisher does not hold the type-I risk if severe nonnormality of the variables’ distributions is given.

AB - There is a big lack of knowledge as concerns a test of the null hypothesis H0: 0 < ρ ≤ ρ0. Usually a test applies by some z-statistic according to Fisher (1921), which is approximately normally distributed. However, there is no evidence of whether the approximation is actually good enough—that is, it is of interest how the factual distribution of the respective test statistic holds the type-I risk—and which type-II risk results. Because this question cannot be answered theoretically at present, we try a simulation study in order to gain respective knowledge. For this, we even investigate the case of variables that are not (at all) normally distributed. Moreover, we consider variables not normally distributed but test the simple case of the exact t-test of H0: ρ = ρ0. The results show, in particular, that the test tracing back to R. A. Fisher does not hold the type-I risk if severe nonnormality of the variables’ distributions is given.

KW - Fleishman system of distributions

KW - Triangular sequential test

KW - correlation coefficient

KW - nonnormality

KW - robustness

UR - http://www.scopus.com/inward/record.url?scp=85009740572&partnerID=8YFLogxK

U2 - 10.1080/15598608.2016.1263810

DO - 10.1080/15598608.2016.1263810

M3 - Article

SN - 1559-8616

VL - 11

SP - 393

EP - 401

JO - Journal of Statistical Theory and Practice

JF - Journal of Statistical Theory and Practice

IS - 3

ER -