Like a chi-square distribution, an F-distribution can only have positive values.An F-distribution is defined by two parameters, i.e., degrees of freedom of the numerator ( \(m\)) and degrees of freedom of the denominator ( \(n\)).An F-distribution is an asymmetrical distribution (skewed to the right).The following are the properties of an F-distribution: The more the degrees of free increase, the more the distribution assumes the shape of a standard normal distribution.Īn F-distribution is used to test the equality of variances of two normally distributed populations from two independent random samples. The shape of a chi-square distribution changes with the change in the degrees of freedom. For each degree of freedom, there are different chi-square distributions.Hence, it is a non-negative distribution. A chi-square distribution is the sum of the squares of \(k\) independent standard normally distributed random variables.A chi-square distribution is defined by one parameter: Degrees of freedom (df), \(v = n – 1\).A chi-square distribution is a non-symmetrical distribution (skewed to the right).In a summary, the following are the properties of a chi-square distribution: Intuitively, chi-square distributions take only non-negative random variables.Ī chi-square distribution is used to test the variance of a population that is distributed normally. A chi-square distribution with \(v\) degrees of freedom is the distribution of the sum of the squares of \(v\) independent standard normally distributed random variables. A chi-square distribution is an asymmetrical family of distributions.
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