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The Pearson's chi-squared test statistic is defined as . The p-value of the test statistic is computed either numerically or by looking it up in a table. If the p-value is small enough (usually p < 0.05 by convention), then the null hypothesis is rejected, and we conclude that the observed data does not follow the multinomial distribution.
Chi-squared distribution, showing χ2 on the x -axis and p -value (right tail probability) on the y -axis. A chi-squared test (also chi-square or χ2 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 ...
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. Unfortunately, Yates's correction may tend to overcorrect.
Pearson's correlation coefficient, when applied to a sample, is commonly represented by and may be referred to as the sample correlation coefficient or the sample Pearson correlation coefficient. We can obtain a formula for r x y {\displaystyle r_{xy}} by substituting estimates of the covariances and variances based on a sample into the formula ...
Relation to the chi-squared test. The commonly used chi-squared tests for goodness of fit to a distribution and for independence in contingency tables are in fact approximations of the log-likelihood ratio on which the G-tests are based. The general formula for Pearson's chi-squared test statistic is
The chi-squared distribution has numerous applications in inferential statistics, for instance in chi-squared tests and in estimating variances. It enters the problem of estimating the mean of a normally distributed population and the problem of estimating the slope of a regression line via its role in Student's t-distribution .
The Cochran–Armitage test for trend, [1] [2] named for William Cochran and Peter Armitage, is used in categorical data analysis when the aim is to assess for the presence of an association between a variable with two categories and an ordinal variable with k categories. It modifies the Pearson chi-squared test to incorporate a suspected ...
D'Agostino's. K. -squared test. In statistics, D'Agostino's K2 test, named for Ralph D'Agostino, is a goodness-of-fit measure of departure from normality, that is the test aims to gauge the compatibility of given data with the null hypothesis that the data is a realization of independent, identically distributed Gaussian random variables.