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These are the answers for a problem was assigned. I came up with, does anybody see anything wrong with any of them? Please let me know if there is
What does balanced mean?
Means that every cell has the same number of observations
What is the difference between completely randomized design and a blocked design, include which one would block?
A completely randomized design consists of a design where the subjects are assigned completely randomly to the groups. A blocked design, on the other hand, corresponds to a design where the subjects are divided into categorized groups with the main purpose of reducing the variance.
What is the model? Explain, what each term represents and what assumptions, if any, are usually made?
This is a two-way factorial ANOVA. We have two factors A and B, and we have a number of replications for each, which means that the interaction term A*B can also be analyzed. The assumptions made are pretty much the same as for a one way ANOVA: It is assumed that the subjects are assigned randomly and independently to the groups. Also we require normality and homogeneity of variances.
What are the hypotheses to be tested?
That the null hypotheses are correct:
for all i, and j
where are the interaction parameters, are the main effects for factor A and are the main effects for factor B.
Complete the following table:
Source:
A Degrees of Freedom: 2 Sum of Squares: 308.25 Mean of Squares: 154.13 F: 8.31 p-value: 0.00061
B Degrees of Freedom: 4 Sum of Squares: 480.52 Mean of Squares: 120.13 F: 6.48 p-value: 0.000188
AB Degrees of Freedom: 8 Sum of Squares: 130.1 Mean of Squares: 16.26 F: 0.88 p-value: 0.51
Error Degrees of Freedom: 65 Sum of Squares: 1205.27 Mean of Squares: 18.54
Total Degrees of Freedom: 79 Sum of Squares: 2124.14
The values in red are the values I came up with
Since this is a balanced design, how many observations are made at each combination of A and B?
There are 3x5 = 15 cells and 80 observations, so each cell has 6 replications.
This is the answer I came up with, but since the number of total observations is 80 (since ijk-1=79), wouldn't the degrees of freedom have to be 89?
Using the p-values you obtained, state what you would do next.
We have to check whether or not the factors A and B (and their interaction) are significant.
What are your conclusions (expressed for a non-statistician)?
The conclusion in that both factors A and B are significant (p < 0.01), but the interaction AB is not (p > 0.1).
Now assume the p-value for AB is significant. Restate your conclusions.
In that case, the significance of each individual factor is disregarded, because now their effects are interrelated.
Last edited by i405 (2008-04-27 21:17:53)
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