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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degrees of freedom if the samples of sizes m1 and m2 are drawn from normal populations with equal variances.