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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 simplest chi-squared distribution is the square of a standard normal distribution. So wherever a normal distribution could be used for a hypothesis test, a chi-squared distribution could be used. Suppose that Z {\displaystyle Z} is a random variable sampled from the standard normal distribution, where the mean is 0 {\displaystyle 0} and the ...
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. = =
The chi-squared statistic can then be used to calculate a p-value by comparing the value of the statistic to a chi-squared distribution. The number of degrees of freedom is equal to the number of cells , minus the reduction in degrees of freedom, . The chi-squared statistic can be also calculated as
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chi-square distribution F_k(x) = \int_0^x t^(n/2-1) * exp(-t/2) / (2^(n/2) * gamma(n/2)) dt from Wikimedia Commons plot-range: 0 to 8 plotted with cubic bezier-curves the bezier-controll-points are calculated to give a very accurate result. accuracy is 0.00001 units symbols in "Computer Modern" (TeX) font embedded created with a plain text ...
It is the distribution of the positive square root of a sum of squared independent Gaussian random variables. Equivalently, it is the distribution of the Euclidean distance between a multivariate Gaussian random variable and the origin. The chi distribution describes the positive square roots of a variable obeying a chi-squared distribution.
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. [2] [3]