The critical value is found in a table, it is a measure of the probability density function.
I'm not quite sure what you are asking, but I will give you an example and hope it helps.
Suppose we have the following table with the values included:
To get some of these values, we can do a few things:
SS total = SS between + SS within = 16.93 (from the table).
To calculate df between:
k - 1 = 3 - 1 = 2
Note: k = number of levels.
To calculate df within:
N - k = 15 - 3 = 12
Note: N = total number of values in all levels.
df total = df between + df within = 14 (from the table).
To calculate MS between:
SS between/df between = (8.13)/2 = 4.065
To calculate MS within:
SS within/df within = (8.8)/12 = 0.73
To calculate F-ratio:
MS between/MS within = (4.065)/(0.73) = 5.57
I hope this will help.
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