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A chi-squared test (also chi-square or χ 2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical variables ( two dimensions of the contingency table ) are independent in influencing the test statistic ...
The chi-squared test, when used with the standard approximation that a chi-squared distribution is applicable, has the following assumptions: [7] Simple random sample The sample data is a random sampling from a fixed distribution or population where every collection of members of the population of the given sample size has an equal probability ...
The chi-squared distribution is used in the common chi-squared tests for goodness of fit of an observed distribution to a theoretical one, the independence of two criteria of classification of qualitative data, and in finding the confidence interval for estimating the population standard deviation of a normal distribution from a sample standard ...
In assessing whether a given distribution is suited to a data-set, the following tests and their underlying measures of fit can be used: Bayesian information criterion; Kolmogorov–Smirnov test; Cramér–von Mises criterion; Anderson–Darling test; Berk-Jones tests [1] [2] Shapiro–Wilk test; Chi-squared test; Akaike information criterion ...
where χ 2 is computed as in Pearson's chi-squared test, and N is the grand total of observations. φ varies from 0 (corresponding to no association between the variables) to 1 or −1 (complete association or complete inverse association), provided it is based on frequency data represented in 2 × 2 tables.
This reduces the chi-squared value obtained and thus increases its p-value. The effect of Yates's correction is to prevent overestimation of statistical significance for small data. This formula is chiefly used when at least one cell of the table has an expected count smaller than 5.
1900: Karl Pearson develops the chi squared test to determine "whether a given form of frequency curve will effectively describe the samples drawn from a given population." Thus the null hypothesis is that a population is described by some distribution predicted by theory.
In statistics, minimum chi-square estimation is a method of estimation of unobserved quantities based on observed data. [1]In certain chi-square tests, one rejects a null hypothesis about a population distribution if a specified test statistic is too large, when that statistic would have approximately a chi-square distribution if the null hypothesis is true.