Correlation Coefficient: Tables for Exact Test and Other Related Considerations

By Jyh-Jiuan Lin, Ching-Hui Chang and Nabendu Pal .

Abstract: Tables of critical values for the exact test method based on the maximum likelihood estimator (MLE) have been obtained to test a hypothesis on the correlation coefficient between the components of a bivariate normal random vector. The exact test is then compared, in terms of size and power, with the other popular methods, namely - the ‘z - test’, the ‘modified z - test’ and the ‘t - test’. While these popular methods have almost identical size and power to the exact test for large samples, their small sample performance is far from satisfactory as evident from our extensive numerical computations. Thus, our tables of critical values are useful when sample size is not large (i.e., _ 30 ). Also, it is demonstrated through a real-life dataset how the tables of critical values can be used for interval estimation.

Key Words: Size, power, confidence interval, asymptotic variance

Authors:
Jyh-Jiuan Lin,
Ching-Hui Chang ,
Nabendu Pal, nxp3695@louisiana.edu

Editor: Sanku Dey, sanku_dey2k2003@yahoo.co.in

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