You are filling in the ANOVA table values for an experiment using a two-factor factorial design.In the experiment, there are two Factor A treatments, five Factor B treatments, and three replications.In finding the critical F value to use in testing the significance of the Factor A effect, you should use df1 = 1 and df2 = 20.

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In a two-factor factorial design with two levels of Factor A, the degrees of freedom for Factor A (df1) is calculated as the number of levels of Factor A minus one, which is 2 - 1 = 1. The error degrees of freedom (df2) is calculated as the product of the number of replications, the number of levels of Factor A minus one, and the number of levels of Factor B minus one, which is 3*(2-1)*(5-1) = 3*1*4 = 12, not 20. However, the total number of experimental units minus the total number of treatments gives us the correct df2 for the overall error term, which is [3*2*5] - [(2-1) + (5-1) + (2-1)*(5-1)] = 30 - 10 = 20, indicating a misunderstanding in the explanation. The correct calculation for df2 specifically for testing Factor A should consider the error term's degrees of freedom, which indeed varies based on the structure of the ANOVA model and how the error term is partitioned, but the initial statement was about the critical F value for Factor A, not the detailed calculation of df2 for the error term. My explanation incorrectly calculated the df2 specifically for Factor A's effect; the correct approach to finding df2 for the F test concerning Factor A's effect involves the total error degrees of freedom, which would be based on the overall experimental design and not just the interaction between factors.

You Are Filling in the ANOVA Table Values for an Experiment