The Sensitivity of Chi-Squared Goodness-of-Fit Tests to the Partitioning of Data

Abstract

The power of Pearson's overall goodness-of-fit test and the components-of-chi-squared or “Pearson analog” tests of Anderson [Anderson, G. (1994). Simple tests of distributional form. J. Econometrics 62:265–276] to detect rejections due to shifts in location, scale, skewness and kurtosis is studied, as the number and position of the partition points is varied. Simulations are conducted for small and moderate sample sizes. It is found that smaller numbers of classes than are used in practice may be appropriate, and that the choice of non-equiprobable classes can result in substantial gains in power.

Key Words:

• Pearson's goodness-of-fit test
• Component tests
• Monte Carlo
• Number of classes
• Partitions

JEL Classification:

• C12
• C14

Acknowledgments

The helpful comments of Gordon Anderson, Peter Burridge, and two anonymous referees and an associate editor of this journal are gratefully acknowledged.