Correlation Coefficient: Tables for Exact Test and Other Related Considerations
By Jyh-Jiuan Lin, Ching-Hui Chang and Nabendu Pal
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.
Size, power, confidence interval, asymptotic variance
Nabendu Pal, firstname.lastname@example.org
Sanku Dey, email@example.com
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