Two-Way RM ANOVA

Question 1

Two-Way RM ANOVA

Answer 1

An analysis of variance with two nominal IVs, one interval ratio DV, and the IV levels are related.

Question 2

Main effect

Answer 2

Direct influence of IV on DV

Question 3

Interaction

Answer 3

Effect of IV1 in the presence of IV2

Question 4

Sources

Answer 4

1. IV1
2. IV1-error
3. IV2
4. IV2-error
5. IV1 x IV2
6. IV2 x IV2-error
7. Ss
8. Ss-error
9. Total

Question 5

df(IV1)

Answer 5

k(IV1) - 1

Question 6

df(IV1-e)

Answer 6

df(IV1) * df(Ss-e)

Question 7

df(IV2)

Answer 7

k(IV2) - 1

Question 8

df(IV2-e)

Answer 8

df(IV2) * df(Ss-e)

Question 9

df(IV1xIV2)

Answer 9

df(IV1) * df(IV2)

Question 10

df(IV1xIV2-e)

Answer 10

df(IV1xIV2) * df(Ss-e)

Question 11

df(Ss)

Answer 11

of IVs - 1

Question 12

df(Ss-e)

Answer 12

N - 1

Question 13

df(Total)

Answer 13

(k[IV1] * k[IV2] * N) - 1

Question 14

MS(IV1)

Answer 14

SS(IV1)/df(IV1)

Question 15

MS(IV1-e)

Answer 15

SS(IV1-e)/df(IV1-e)

Question 16

MS(IV2)

Answer 16

SS(IV2)/df(IV2)

Question 17

MS(IV2-e)

Answer 17

SS(IV2-e)/df(IV2-e)

Question 18

MS(IV1xIV2)

Answer 18

SS(IV1xIV2)/df(IV1xIV2)

Question 19

MS(IV1xIV2-e)

Answer 19

SS(IV1xIV2-e)/df(IV1xIV2-e)

Question 20

F(IV1)

Answer 20

MS(IV1)/MS(IV1-e)

Question 21

F(IV2)

Answer 21

MS(IV2)/MS(IV2-e)

Question 22

F(IV1xIV2)

Answer 22

MS(IV1xIV2)/MS(IV1xIV2-e)

Question 23

Two-Way RM ANOVA Hypothesis Test Steps

Answer 23

1. Calculate F-ratios (will have 3)
2. Set criteria for decisions
3. Make decisions regarding significance
4. Interpret (w/ comparisons if needed)

Question 24

Set criteria for decisions

Answer 24

df(IV1) = df between (numerator), dfIV1-e = df w/in (denominator) for locating F[crit] of IV1
dfIV2 = df between (numerator), dfIV2-e = df w/in (denominator) for locating F[crit] of IV2
dfIV1xIV2 = df between (numerator), dfIV1xIV2-e = df w/in (denominator) for locating F[crit] of IV1xIV2

Question 25

Make decisions regarding significance

Answer 25

If F > F[crit] (falls within critical boundary), reject H0 and conclude that there is a significant effect (or interaction).
If F < F[crit] (falls outside critical boundary), retain H0 and conclude that there is not a significant effect (or interaction). Draw table to plot F-ratio and F[crit] to help you determine whether the F-ratio falls within the critical boundary F[crit].

Question 26

Interpret (w/ comparisons if needed)

Answer 26

Go back to question and ask: what is my IV, and what is my DV? Look at the # of levels to determine if you need to do a comparison test (3+ levels) of if you can compare the means directly to each other (2 levels)

Question 27

Significant main effect

Answer 27

1. k = 2: Interpret significant mean differences in context of problem
2. k = 3+: Run a Tukey or a priori comparison test, then interpret significant mean differences in context of problem

Question 28

Significant interaction

Answer 28

1. Conduct simple effects
2. k = 2 in simple effects ANOVAs: interpret significant mean differences in context of problem
3. k = 3+ in simple effects ANOVAs: Run a Tukey or a priori comparison test, then interpret significant mean differences in context of problem

Question 29

No significant result

Answer 29

Interpret in context of problem

Question 30

Calculate F-ratio steps

Answer 30

1. Calculate SS (will be provided)
2. Calculate dfs (9)
3. Calculate MSs (6)
4. Calculate F-ratios (3)