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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 .
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 ...
Chi is the basis for the name literary chiastic structure and the name of chiasmus. Symbolism [ edit ] In Plato 's Timaeus , it is explained that the two bands that form the soul of the world cross each other like the letter Χ.
The chi-squared test, when used with the standard approximation that a chi-squared distribution is applicable, has the following assumptions: 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 of ...
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 .
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.
It is thus related to the chi-squared distribution by describing the distribution of the positive square roots of a variable obeying a chi-squared distribution. If Z 1 , … , Z k {\displaystyle Z_{1},\ldots ,Z_{k}} are k {\displaystyle k} independent, normally distributed random variables with mean 0 and standard deviation 1, then the statistic
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 λ / 2 {\displaystyle \lambda /2} , and the conditional distribution of Z given J = i is chi-squared with k + 2 i degrees of freedom.