In an ANOVA, what does F=1 mean?

1 Answer
Mar 5, 2016

When using a F-test to compare variances, a value of #F=1# implies that the two variances are equal.


An F-test is used to test if the variances of two populations are equal. The statistic we define to test this is the ratio of the two variances:

#F = s_1^2/s_2^2#

Where #s_1# and #s_2# are the sample variances. The further this value deviates from 1, the more likely that the underlying variances are actually different. The F-distribution is used to quantify this likelihood for differing sample sizes and the confidence or significance we would like the answer to hold.

A value of #F=1# means that no matter what significance level we use for the test, we will conclude that the two variances are equal.

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