F-distribution: theoretical distribution that compares two populations
There are two sets of degrees of freedom; one for the numerator and one for the denominator.
To calculate the F ratio, two estimates of the variance are made.
Variance between samples: An estimate of σ2 that is the variance of the sample means multiplied by n (when the sample sizes are the same.).
Variance within samples: An estimate of σ2 that is the average of the sample variances (also known as a pooled variance).
MS means: "mean square."
MSbetween: is the variance between groups
MSwithin: is the variance within groups.
In order to perform a F test of two variances, it is important that the following are true:
F has the distribution F ~ F(n1 – 1, n2 – 1)
where n1 – 1 are the degrees of freedom for the numerator and n2 – 1 are the degrees of freedom for the denominator.
F is close to one: the evidence favors the null hypothesis (the two population variances are equal)
F is much larger than one: then the evidence is against the null hypothesis
A test of two variances may be left, right, or two-tailed.
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