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In probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables.
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 ...
chi. In probability theory and statistics, the chi distribution is a continuous probability distribution over the non-negative real line. 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 ...
Pearson's chi-squared test is used to assess three types of comparison: goodness of fit, homogeneity, and independence . A test of goodness of fit establishes whether an observed frequency distribution differs from a theoretical distribution. A test of homogeneity compares the distribution of counts for two or more groups using the same ...
The resulting value can be compared with a chi-square distribution to determine the goodness of fit. The chi-square distribution has ( k − c) degrees of freedom, where k is the number of non-empty cells and c is the number of estimated parameters (including location and scale parameters and shape parameters) for the distribution plus one.
A chi-squared distribution with 2 degrees of freedom ( k = 2) is an exponential distribution with a mean value of 2 (rate λ = 1/2 .) A Weibull distribution with shape parameter k = 1 and rate parameter β is an exponential distribution with rate parameter β.
Generalized chi-squared distribution. In probability theory and statistics, the generalized chi-squared distribution (or generalized chi-square distribution) is the distribution of a quadratic form of a multinormal variable (normal vector), or a linear combination of different normal variables and squares of normal variables.
Reduced chi-squared statistic. 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.