Module 12: 2 Factor ANOVA

Question 1

2 factor ANOVA use

Answer 1

-for 2 categorical variables on a numerical variable

Question 2

ANOVA questions

Answer 2

-main effects A: differences of level factor A among all levels of factor B
-main effects B: differences of level factor B among all levels of factor A
-interaction: cell by cell comparisons

Question 3

Interaction and additivity

Answer 3

-interaction is any deviation from additivity

Question 4

Interaction plot

Answer 4

-y axis shows numerical variable
-x axis shows the levels of one categorical variable
-lines are used to connect cells across x axis according to levels of other categorical variable
-if parallel = no interaction
-if not parallel = interaction

Question 5

2 factor anova null and alternative

Answer 5

-main effects a
-Ho: ua1 = ua2 ….
-Ha: ua1 =/ ua2 …

-main effects b
-Ho: ub1 = ub2 ….
-Ha: ub1 =/ ub2 …..

-interaction
-Ho: Da1b1 = Da1b2 ….. = 0
-Ha: Da1b1 =/ Da1b2 …. =/0

Question 6

Sources of variation ANOVA calculations

Answer 6

-group variation factor a: MSa = SSa / dfa
-dfa is a-1, where a is number of levels in factor
-SSa is total group variation

-group variation factor b: MSb = SSb / dfb
-dfb is b-1, where b is number of levels in factor

-AB interaction: MSab = SSab / dfab
-dfab is (a-1)(b-1)

-residual variation: MSe = SSe / dfe
-dfe is ab(n-1) where n is

Question 7

F test ANOVA calculations

Answer 7

-main effects a: F= MSa / Mse
-main effects b: F= MSb / MSe
-interactions: F= MSab /MSe

Question 8

Scientific conclusions of 2 factor ANOVA

Answer 8

-first evaluate interaction
-only evaluate main effects if fail to reject null hypothesis