Distribution of the Chi-Squared Test in Nonstandard Situations

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...

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...

Notes on the chi-squared distribution

A Bayesian Chi-Squared Test for Hypothesis Testing

A new Bayesian test statistic is proposed to test a point null hypothesis based on a quadratic loss. The proposed test statistic may be regarded as the Bayesian version of Lagrange multiplier test. Its asymptotic distribution is obtained based on a set of regular conditions and follows a chi-squared distribution when the null hypothesis is correct. The new statistic has several important advant...

Differentially Private Chi-squared Test by Unit Circle Mechanism

We describe Algorithm 2 in detail. Algorithm 2 takes as input the sample set S, the query sequence F , the sensitivity of query ∆, the threshold τ , and the stop parameter s. Algorithm 2 outputs the result of each comparison with the threshold. In Algorithm 2, each noisy query output is compred with a noisy threshold at line 4 and outputs the result of comparison. Let ⊤ mean that fk(S) > τ . Al...