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The simplest chi-squared distribution is the square of a standard normal distribution. So wherever a normal distribution could be used for a hypothesis test, a chi-squared distribution could be used. Suppose that Z {\displaystyle Z} is a random variable sampled from the standard normal distribution, where the mean is 0 {\displaystyle 0} and the ...
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
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 square of a standard normal random variable has a chi-squared distribution with one degree of freedom. If X is a Student’s t random variable with ν degree of freedom, then X 2 is an F (1,ν) random variable. If X is a double exponential random variable with mean 0 and scale λ, then |X| is an exponential random variable with mean λ.
The "step" line relates to Chi-Square test on the step level while variables included in the model step by step. Note that in the output a step chi-square, is the same as the block chi-square since they both are testing the same hypothesis that the tested variables enter on this step are non-zero.
Since a non-central chi-squared variable is a sum of squares of normal variables with different means, the generalized chi-square variable is also defined as a sum of squares of independent normal variables, plus an independent normal variable: that is, a quadratic in normal variables.
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 .
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 .