The Yates' correction factor in chi-squared analyses

Information Divergence is more chi squared distributed than the chi squared statistics

For testing goodness of fit it is very popular to use either the χ-statistic or G-statistics (information divergence). Asymptotically both are χ-distributed so an obvious question is which of the two statistics that has a distribution that is closest to the χ-distribution. Surprisingly, when there is only one degree of freedom it seems like the distribution of information divergence is much bet...

CHI-Squared Test of Independence

Chi-square (X) test is a nonparametric statistical analyzing method often used in experimental work where the data consist in frequencies or ‘counts’ – for example the number of boys and girls in a class having their tonsils out – as distinct from quantitative data obtained from measurement of continuous variables such as temperature, height, and so on. The most common use of the test is to ass...

Notes on the chi-squared distribution

Optimal correction for continuity and conditions for validity in the unconditional chi-squared test

The most usual asymptotic unconditional method for comparing two independent binomial proportions is the chi-squared test. There are various versions of it (with or without continuity corrections), but there has been no exhaustive study about how they behave, about their optimality, nor about the conditions under which the approximation is considered reliable. In this paper these queries are ex...

Karl Pearson and the Chi - squared Test

Karl Pearson was a man of many parts: the applied mathematician who completed Todhunter's History of the Theory of Elasticity; the philosopher of science whom Lenin described as 'this conscientious and honest opponent of materialism' (1970, p. 170); the statistician who espoused the cause of evolution and edited Biometrika for 35 years; the innovator and administrator whose Department became fa...