![]() ![]() StatsDirect calculates the probability associated with a chi-square random variable with n degrees of freedom, for this a reliable approach to the incomplete gamma integral is used ( Shea, 1988). As the expected value of chi-square is n-1 here, the sample variance is estimated as the sums of squares about the mean divided by n-1. The number of linear constraints associated with the design of contingency tables explains the number of degrees of freedom used in contingency table tests ( Bland, 2000).Īnother important relationship of chi-square is as follows: the sums of squares about the mean for a normal sample of size n will follow the distribution of the sample variance times chi-square with n-1 degrees of freedom. If there are m linear constraints then the total degrees of freedom is n-m. Here the sum of the squares of z follows a chi-square distribution with n-1 degrees of freedom. ![]() The sub-set is defined by a linear constraint: The so called "linear constraint" property of chi-square explains its application in many statistical methods: Suppose we consider one sub-set of all possible outcomes of n random variables (z). A chi-square with many degrees of freedom is approximately equal to the standard normal variable, as the central limit theorem dictates. Menu location: Analysis_Distributions_Chi-Square.Ī variable from a chi-square distribution with n degrees of freedom is the sum of the squares of n independent standard normal variables (z).Ī chi-square variable with one degree of freedom is equal to the square of the standard normal variable. ![]()
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