Assume that 100 subjects received one of four treatment combinations and produced the data reported below. Conduct a two-factor ANOVA and complete an ANOVA table reporting the relevant SS, df, MS, F's.
N=100 n=25
the table shows A1 and A2 at the top and B1 and B2 on the side. Under A1 it shows the means : 100 and 40 goind down. Next to that is the variance 900 and 800 going down. Then for A2 the mean is 70 and 60 and the variance is 700 and 1200.
I am having trouble finding the s2 Total. I do not know what to do.
Nevermind I figured it out
To find the sum of squares for the total (s2 Total), you need to use the formula:
s2 Total = SS Total / df Total
To calculate SS Total, you first need to calculate the sum of squares for each factor (A and B) and their interaction (A x B). The sum of squares for each factor is calculated by summing the squared deviations from the overall mean for each level within the factor. The formula is:
SS Factor = ∑ (ni * (Mij - M)^2)
where ni is the number of observations for each level, Mij is the mean for each level, and M is the overall mean.
For the interaction term, the formula is:
SS Interaction = ∑ (ni * (Mij - Mi - Mj + M)^2)
where ni is the number of observations for each combination of levels, Mij is the mean for each combination, Mi is the mean for level i, Mj is the mean for level j, and M is the overall mean.
Once you have calculated SS Total, which is the sum of squares for the total, you can determine the appropriate degrees of freedom (df Total) based on the sample size. In this case, you have N = 100 subjects, so df Total = N - 1 = 100 - 1 = 99.
Finally, you can find s2 Total by dividing SS Total by df Total.
It's important to note that without specific values for each combination of treatments (A1B1, A1B2, A2B1, A2B2), it's not possible to provide a specific calculation. However, the steps outlined above should help you determine the sum of squares for the total given the available data.