In some complicated settings, such as unbalanced split-plot designs, the sums-of-squares no longer have scaled chi-squared distributions.
42.
Under the null hypothesis, this statistic has asymptotically the chi-squared distribution with the number of degrees of freedom equal to the rank of matrix.
43.
But the numerator then has a noncentral chi-squared distribution, and consequently the quotient as a whole has a non-central F-distribution.
44.
Certain assumptions must be met for the statistic to follow a chi-squared distribution, and often empirical " p "-values are computed.
45.
*One can generate Student-t samples by taking the ratio of variables from the normal distribution and the square-root of chi-squared distribution.
46.
An additional reason that the chi-squared distribution is widely used is that it is a member of the class of likelihood ratio tests ( LRT ).
47.
Scaling a value that follows an exponential distribution by a factor of two yields a quantity that follows a chi-squared distribution with two degrees of freedom.
48.
The fit of chi square distribution depends on the degrees of freedom ( df ) with good agreement with df = 1 and decreasing agreement as the df increases.
49.
Equivalently, this distribution results from compounding a Gaussian distribution with a scaled-inverse-chi-squared distribution with parameters \ nu and \ sigma ^ 2.
50.
The log rank statistic has a chi-squared distribution with one degree of freedom, and the p-value is calculated using the chi-squared distribution.
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