Chp 8: Factorial Design Flashcards
What is factorial treatment structure?
Where g treatments are comprised of all factor-level combinations of 2 (or more) factors
In a balanced design, with more than two factors, what is the total sample size N?
abn
where a is the levels in factor 1
b is the levels in factor 2
n is the number of experimental units in each combo
How many parameters are there in a balanced design with more than two factors?
a*b
What is the interaction of factors A and B?
The effect of A on Y which depends on B
Denoted:
alphaß_ij
What parameters do we have in the mean effects model with more than one factor?
What constraints do we have?
µ
a
b
alphaß
When visually checking interactions, we check to see that…
The lines are roughly parallel
If they aren’t parallel, we’ll look for how and where they are not parallel. This suggests a true interaction!
What does it mean if two factors are “crossed”?
It means g treatments are comprised of all factor-level combinations of 2 (or more) factors
What is a two-way ANOVA?
When the factors are crossed
If an interaction tests as significant, then…
Consider two interaction plots to see how the interaction is significant!
- It looks at the means for each “cross” of the levels of the interactions
- which points in the interaction plot are causing the non-parallel-ness?
If an interaction (AB) does not test as significant, then…
1) Look at the main effects (A,B)
2) If A or B test significan, do posthoc tests to characterize (pairwise comparisons, adjusted for multiple comparisons)
When can we use REGWQ?
When it’s a balanced design with just one factor.
What do we use if we can’t use REGWQ?
Tukey test!
How do we get a partial R^2?
SS_effect / SS_total
When can we partition an R^2 into a partial R^2?
When we have a balanced design.
