Transformations with Improved Chi-Squared Approximations

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...

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...

Decomposing compositional data: minimum chi-squared reduced-rank approximations on the simplex

The logratio transformation (Aitchison, 1981, 1986) opened the way to statistically rigorous analysis of compositional data. Most statistical problems in compositional data analysis can be formulated in terms of logratios, and solved accordingly. However, some problems are more easily described and solved in terms of raw compositional variables. Raw compositions with k components are restricted...

A comparison of efficient approximations for a weighted sum of chi-squared random variables

Inmany applications, the cumulative distribution function (cdf) FQN of a positively weighted sum of N i.i.d. chi-squared randomvariables QN is required.Although there is no known closed-form solution for FQN , there are many good approximations. When computational efficiency is not an issue, Imhof’smethod provides a good solution. However, when both the accuracy of the approximation and the spe...

Chi squared automatic interaction detector pdf