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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 number of degrees of freedom is equal to the number of cells rc, minus the reduction in degrees of freedom, p, which reduces to (r − 1)(c − 1). For the test of independence, also known as the test of homogeneity, a chi-squared probability of less than or equal to 0.05 (or the chi-squared statistic being at or larger than the 0.05 ...
The name "chi-square" ultimately derives from Pearson's shorthand for the exponent in a multivariate normal distribution with the Greek letter Chi, writing −½χ 2 for what would appear in modern notation as −½x T Σ −1 x (Σ being the covariance matrix). [27]
In statistics, Yates's correction for continuity (or Yates's chi-squared test) is used in certain situations when testing for independence in a contingency table.
The p-value for the significance of V is the same one that is calculated using the Pearson's chi-squared test. [citation needed] The formula for the variance of V=φ c is known. [3] In R, the function cramerV() from the package rcompanion [4] calculates V using the chisq.test function from the stats package.
Consider the k samples to represent a single point in a k-dimensional space.The chi square distribution for k degrees of freedom will then be given by: = = (()) = (+ + +) / / ...
Such measures can be used in statistical hypothesis testing, e.g. to test for normality of residuals, to test whether two samples are drawn from identical distributions (see Kolmogorov–Smirnov test), or whether outcome frequencies follow a specified distribution (see Pearson's chi-square test).
In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation ( MSWD ) in isotopic dating [ 1 ] and variance of unit weight in the context of weighted least squares .