F-distribution

What is the F-distribution?

The F-distribution is a continuous sampling distribution of two independent random variables with chi-square distributions, each divided by its degrees of freedom.

Use the F-distribution when a test statistic is the ratio of two variables that each have a chi-square distribution. For example, use the F-distribution in the analysis of variance and in hypothesis testing to determine whether two population variances are equal.

Calculate probabilities for an F-distribution with infinite denominator degrees of freedom

Suppose X follows an F-distribution with 5 numerator degrees of freedom and infinite denominator degrees of freedom, and you want the probability that X is less than or equal to 2. You can find the probability that Y is less than or equal to 2, where Y follows an F-distribution with 5 numerator and 99999 denominator degrees of freedom and Y approximates X.

1. Choose Calc > Probability Distributions > F.
2. In Numerator degrees of freedom, enter 5.
3. In Denominator degrees of freedom, enter 99999.
4. Choose Input constant and enter 2. Click OK.
The CDF for 2 is 0.924755. This value gives the area under the curve up to 2.
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