F Distribution:

The F distribution is a family of distributions differentiated by two parameters: m₁ (degrees of freedom, numerator) and m₂ (degrees of freedom, denominator). If x₁ and x₂ are independent random variables with a chi-square distribution with m₁ and m₂ degrees of freedom respectively, then the random variable f = (x₁/m₁)/(x₂/m₂) has an F distribution with (m₁,m₂) degrees of freedom.

The F-distribution arises naturally in tests for comparing variances of two populations. The ratio of two sample variances has an F-distribution with degrees of freedom if the samples of sizes m₁ and m₂ are drawn from normal populations with equal variances.

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