Question

Give an explanation of the F statistic. Explain the shape of the F distribution.

Answer 1

The F-distribution is a family of distributions.The particular F-distribution that we use for an application depends upon the number of degrees of freedom that our sample has. This feature of the F-distribution is similar to both the t-distribution and the chi-square distribution. A Statistical F Test uses an F Statistic to compare two variances, s1 and s2, by dividing them. The result is always a positive number (because variances are always positive).We always test that the population variances are equal when running an F Test. In other words, you always assume that the variances are equal to 1. Therefore, your null hypothesis will always be that the variances are equal.

Shape of F distribution

?The F-distribution is either zero or positive, so there are no negative values for F. The F-distribution is skewed to the right. Thus this probability distribution is non-symmetrical. This feature of the F-distribution is similar to the chi-square distribution.