From Sums of Squares to F

A one-way ANOVA compares the mean apple weight across $k = 3$ orchards, using $5$ apples from each orchard, so $N = 15$ observations in total.

The analysis reports:

Source	Sum of squares	Degrees of freedom
Between groups	$SS_{\text{between}} = 84$	$k - 1$
Within groups	$SS_{\text{within}} = 168$	$N - k$

The F-statistic is the ratio of the between-group mean square to the within-group mean square, where a mean square is a sum of squares divided by its own degrees of freedom.

What is the value of $F$ ?

From Sums of Squares to F

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