2371 NA The log likelihood test statistics have a

chi-square distribution with one degree of freedom.

For some distributions, like t distribution or

Chi-square distribution, the t or Chi-square value depends on a single value of degree of freedom only.

t] is large enough, it is possible to use the Central Limit Theorem to approximate the

Chi-square distribution to a Gaussian distribution [31], and the following approximation holds

dx,[lambda]] is a left-tail non-central

Chi-square distribution with degree of freedom (df) and non-centrality parameter [lambda] = [Nw.

1-[alpha],df] the [alpha]th percentile of the

chi-square distribution with df, degrees of freedom, n is the sample size, df = n - m (number of independent random samples) is degrees of freedom defined as the number of values that are free to vary, and Z(1-P)/2 is the pth percentile of the standard normal distribution.

The

chi-square distribution test and largest normalized residual tests are used to detect and identify the malicious data [11].

The distinct advantage of the prescribed methods is that it circumvents the uncertainty of sample variance by taking account of the underlying

chi-square distribution of sample variance and permits a corrected sample size determination according to the desired assurance probability and expected power considerations.

The calculated statistics is compared with the critical value of the

chi-square distribution.

Results indicate a noncentral

chi-square distribution for rows and columns of the GxE interaction matrix, which was also verified by the Kolmogorov-Smirnov test and Q-Q plot.

An assumption is also made when using the

chi-square distribution as an approximation to the distribution of kh2, is that the frequencies expected under independence should not be "too small".

2] has an asymptotic

chi-square distribution with (C-1) (S-1) degrees of freedom.

The square of a normal N(0, 1) variable has the

chi-square distribution [[chi].