chi-square distribution


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chi-square dis·tri·bu·tion

a variable is said to have a chi-square distribution with K degrees of freedom if it is distributed like the sum of the squares of K independent random variables, each of which has a normal (gaussian) distribution with mean zero and variance one. The chi-square distribution is the basis for many variations of the chi-square(d) test, perhaps the most widely used test for statistical significance in biology and medicine.

chi-square distribution

in statistical terms this is said of a variable with K degrees of freedom if it is distributed like the sum of the squares of K independent random variables each of which has a normal distribution with mean zero and variance of 1.
References in periodicals archive ?
The degrees of freedom for the approximate chi-square distribution of the objective function J([?
p] is a random variable with the scaled chi-square distribution given in Equation 6, the power function defined in Equation 7 is also a random variable.
Furthermore, each of the statistics tested had an asymptotic chi-square distribution.
The chi-square distributions were used to approximate skewed distributions where the chi-square distribution with 6 degrees of freedom is less skewed than the one with 5 degrees of freedom.
Checking the chi-square distribution table in the appendix, we find that with k-1 = 5 degrees of freedom, [chi square] = 11.
If the hypothesis is true the test statistic has approximately chi-square distribution with 57 degrees of freedom.
MVN(0,1), then if A is a symmetric idempotent matrix of rank p, then ZAZ has a chi-square distribution with p degrees of freedom.
e) FDR: false discovery rate (= p-value x N/Rank), where p value is comparison-wise type I error rate (at the point-wise level) taken from chi-square distribution with 1 df, N is number of all tests (47 traits x 48 map points = 2,256), and Rank is the number of the null hypothesis ranked by descending p values across all N tests.
t], n) is the probability that a random observation from the chi-square distribution with n degrees of freedom falls in the interval [0 [X.
The deviance has a limiting chi-square distribution, and so significance is judged by comparison to critical values of the chis-quare distribution.
By applying the above product to any data point, a two-dimensional normal distribution is transformed into a one-dimensional chi-square distribution with two degrees of freedom.