df] is the cumulative distribution function of a

chi-square distribution with df degrees of freedom.

Chi-square distribution table corresponding to a detection confidence with probability and degree of freedom can be obtained as follows:

where [chi square]([upsilon]) is a

chi-square distribution with [upsilon] degrees of freedom.

KEY WORDS / Genotype and Environment Contribution / GxE Interaction / Noncentral

Chi-Square Distribution / Modified F Test /

It is well known that sample variances tend to have a

chi-square distribution (Overall & Woodward, 1974).

Checking the

chi-square distribution table, we find that with k-1 = 5 degrees of freedom, the critical [chi square] = 11.

k)

chi-square distribution with [kappa] = sm (k - (m + 1)/2) degrees of freedom (the number of random variables [Z.

If a random variable X has a

chi-square distribution with m degrees of freedom, and y is an independent chi-square random variable with n degrees of freedom, thenth ratio f = x/m/y/n has an F-distribution with m and n degrees of freedom.

Also, the empirical distribution function of D, found under the null composite hypothesis, follows the theoretical

chi-square distribution function, if not as near.

However, the test statistic with

chi-square distribution of 1 df was used to standardize p values such that the maximum p value should be 1.

Geared toward graduate students and professionals in statistics, engineering, social sciences and medical science but applicable to other fields as well, this text starts with the statistical decision principle and proceeds to normal distribution,

chi-square distribution and properties, discrete distributions, and large sample theory.

2] (n) denotes the

chi-square distribution with n degrees of freedom and [X.

The difference between competitive models has itself a

chi-square distribution with the number of degrees of freedom equal to the corresponding differences in the degrees of freedom of the separate models.

The

chi-square distribution of numbers of plots with 0, 1, 2, etc.