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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]
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
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 .
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 ...
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 .
A generalized chi-square variable or distribution can be parameterized in two ways. The first is in terms of the weights w i {\displaystyle w_{i}} , the degrees of freedom k i {\displaystyle k_{i}} and non-centralities λ i {\displaystyle \lambda _{i}} of the constituent non-central chi-squares, and the coefficients s {\displaystyle s} and m ...
There are several methods to derive chi-squared distribution with 2 degrees of freedom. ... The chi square distribution for k degrees of freedom will then be given by ...
From this representation, the noncentral chi-squared distribution is seen to be a Poisson-weighted mixture of central chi-squared distributions. Suppose that a random variable J has a Poisson distribution with mean /, and the conditional distribution of Z given J = i is chi-squared with k + 2i degrees of