Combining independent tests for a common parameter of several continuous distributions: a new test and power comparisons

Abstract

The problem of testing a common parameter of several independent continuous populations is considered. Among all tests, Fisher’s combined test is the most popular one and is routinely used in applications. In this article, we propose an alternative method of combining the p-values of independent tests using chi-square scores, referred to as the inverse chi-square test. The proposed test is as simple as other existing tests. We compare the powers of the combined tests for (i) testing a common mean of several normal populations, (ii) testing the common coefficient of variation of several normal populations, (iii) testing the common correlation coefficient of several bivariate normal populations, (iv) testing the common mean of several lognormal populations and (v) testing the common mean of several gamma distributions. Our comparison studies indicate that the inverse chi-square test is a better alternative combined test with good power properties. An illustrative example with real-world data is given for each problem.

Keywords:

• Common mean
• Exact test
• Inverse normal
• ${\chi }^2$ score
• Meta analysis
• Power
• z score

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F03
• 62P10

Acknowledgment

The authors are grateful to two reviewers for providing valuable comments and suggestions.

Notes

1 Our values of ${\widehat{\tau }}_1$ and ${\widehat{\tau }}_2$ are based on the means and variances reported in Fung and Tsang (1998). It is not clear how the authors Fung and Tsang (1998) and Tian (2005) obtained the value of 0.0406 for ${\widehat{\tau }}_1$ and the value of 0.0346 for ${\widehat{\tau }}_2.$