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.
To verify adhesion of the sum of squares of the simulated data to the noncentral chi-square distribution
used of the Kolmogorov-Smirnov test.
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.