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Is F significant? If it is significant, at what alpha level?
Given Information :
A new diet pill is being tested for effectiveness . Four groups of women are seleced Women in Group 1 (n=10) are given 5 mg of the drug , those in Group 2 (n=10) are given 10 mg of the drug , Group 3 (n=10) gets 15 mg , and women in Group 4 (n=10) are given a placebo (control). The women are asked to record the percentage of weight lost after taking the pill daily for 6 months .
Sum of squares between treatment is given as = 263.2
Sum of square for error or within treatment is given as = 365.2
Degrees of Freedom :
total degrees of freedom, N-1 = 40-1 = 39
the degrees of freedom for the between group (k-1) and the degrees of freedom for the denominator are the degrees of freedom for the within group (N-k).
How many groups were there in this problem?
Four - one for each drug. So when we are comparing between the groups, there are 3 degrees of freedom. In general, that is one less than the number of groups, since k represents the number of groups, that would be k-1.
How many degrees of freedom were there within the groups. Well, if there are 39 degrees of freedom altogether, and 3 of them were between the groups, then 39-3 = 36 of them are within the groups.
In general terms, that would be (N-1) - (k-1) = N-1-k+1=N-k.
Mean Square :
The variance due to the interaction between the samples is denoted MS(B) for Mean Square Between groups. This is the between group variation divided by its degrees of freedom.
The variance due to the differences within individual samples is denoted MS(W) for Mean Square Within groups. This is the within group variation divided by its degrees of freedom.
Mean Squares = Variances
The variances are found by dividing the variations by the degrees of freedom, so divide the SS(between) = 263.2 by the df(between) = 3 to get the MS (between) = 87.733 and divide the SS(within) = 365.2 by the df(within) = 39 to get the MS(within) = 9.364
F - statistic
Once you have the variances, you divide them to find the F test statistic.
In this case, we will always take the between variance divided by the within variance and it will be a right tail test.
So, divide MS(between) = 87.733 by MS(within) = 9.364 to get F = 9.3692
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