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For the chi-squared distribution, only the positive integer numbers of degrees of freedom (circles) are meaningful. By the central limit theorem, because the chi-squared distribution is the sum of independent random variables with finite mean and variance, it converges to a normal distribution for large .
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.
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 ...
chi square distribution Category: ... accuracy is 0.00001 units symbols in "Computer Modern" (TeX) font embedded created with a plain text editor using GNU/Linux
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 ...
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The term chi-square, chi-squared, or has various uses in statistics: chi-square distribution, a continuous probability distribution; chi-square test, name given to some tests using chi-square distribution; chi-square target models, a mathematical model used in radar cross-section