Improving Accuracy of Goodness-of-fit Test

TL;DR

This paper proposes a method to enhance the accuracy of the chi-square goodness-of-fit test by incorporating two correction terms that depend on the sample size, improving the approximation of the test statistic's distribution.

Contribution

The paper introduces a correction method for the chi-square goodness-of-fit test that accounts for sample size, leading to more precise p-value calculations.

Findings

Improved approximation of the test statistic distribution.

Reduction in type I error rates for small samples.

Enhanced reliability of goodness-of-fit testing.

Abstract

It is well known that the approximate distribution of the usual test statistic of a goodness-of-fit test is chi-square, with degrees of freedom equal to the number of categories minus 1 (assuming that no parameters are to be estimated -- something we do throughout this article). Here we show how to improve this approximation by including two correction terms, each of them inversely proportional to the total number of observations.