Two-Way ANOVA

Question 1

Two-Way ANOVA

Answer 1

An analysis of variance where there are 2 nominal IVs. The IV levels are unrelated, and the DV is interval/ratio. Analysis of variance for a two-way factorial research design.

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. The effect of one IV on DV DEPENDS on the other IV.

Question 4

Determining if there is a main effect

Answer 4

You tell whether there is a main effect by looking at the marginal means. There is a main effect for a particular IV if the marginal means for the different levels of one IV are DIFFERENT from each other.

Question 5

Determining if there is an interaction (cells)

Answer 5

You tell whether there is an interaction effect by looking at the pattern of cell means. There is an interaction effect if the pattern of cell means in one row is DIFFERENT from the pattern of cell means across another row. IGNORE main effects (marginal means) when determining if there is an interaction.

Question 6

Determining interaction by bar graph

Answer 6

Whenever there is an interaction, the pattern of bars on one section of the graph is DIFFERENT from the pattern of bars on the other section of the graph.

Question 7

Marginal mean

Answer 7

In a factorial design in ANOVA, the mean score for all the participants at a particular level of one of the IVs.

Question 8

Grand mean (GM)

Answer 8

Overall mean of all the scores, regardless of what group they are in. The average of the means within a particular group is the grand mean for that group, which is needed for conducting simple effects.

Question 9

Between group variance

Answer 9

Consists of effect of IV1, effect of IV2, effect of IV1 x IV2, and random things (sampling error).

Question 10

Within-group variance

Answer 10

Consists of error variance (sampling error).

Question 11

Total variability

Answer 11

Consists of between group and within group variance.

Question 12

Factor

Answer 12

Independent variable

Question 13

Calculating F-ratio steps

Answer 13

1. Calculate SS’s (may be provided)
2. Calculate df’s (6)
3. Calculate MS’s (4)
4. Calculate F-ratios (3)

Question 14

SS(b/w) formula

Answer 14

SS(b/w) = SS(b/w-IV1) + SS(b/w-IV2) + SS(b/w-IV1 x IV2).

Question 15

SS(BW-IV1) concept

Answer 15

Group’s deviations from the Grand Mean

Question 16

SS(BW-IV2) concept

Answer 16

Group’s deviations from the Grand Mean

Question 17

SS(b/w-IV1 x IV2) formula

Answer 17

SS(b/w-IV1 x IV2) = SS(Total) - SS(b/w-IV1) - SS(b/w-IV2) - SS(w/in)

Question 18

SS(w/in) conceptual

Answer 18

Score’s deviations from their group means

Question 19

SS(Total) formula

Answer 19

SS(Total) = SS(b/w) + SS(w/in)

Question 20

df(B/w)

Answer 20

df(B/w) = df(B/w-IV1) + df(B/w-IV2) + df(B/w-IV1 x IV2)

Question 21

df(IV1)

Answer 21

df(IV1) = k(IV1) - 1

Question 22

df(IV2)

Answer 22

df(IV2) = k(IV2) - 1

Question 23

df(IV1 x IV2)

Answer 23

df(IV1 x IV2) = df(IV1) X df(IV2) (multiply!)

Question 24

df(w/in)

Answer 24

df(Within) = df(Total) - df(b/w)

Question 25

df(Total)

Answer 25

df(Total) = N - 1

Question 26

Order of df calculations for Two-Way ANOVA

Answer 26

1. Calculate df(IV1)
2. Calculate df(IV2)
3. Calculate df(IV1 x IV2)
4. Calculate df(Between)
5. Calculate df(Total)
6. Calculate df(Within)

Question 27

MS formula

Answer 27

MS(x) = SS(x)/df(x)

Question 28

F-Ratio formula

Answer 28

F(x) = MS(x)/MS(w/in)

Question 29

4 MS values

Answer 29

1. MS(IV1)
2. MS(IV2)
3. MS(IV1 x IV2)
4. MS(w/in)

Question 30

3 F-ratio values

Answer 30

1. F-ratio for IV1
2. F-ratio for IV2
3. F-ratio for IV1 x IV2

Question 31

Two-Way ANOVA hypothesis testing steps

Answer 31

1. Compute F-ratios: will have 3.
2. Set criteria for decisions: add F[crit] column to source table.
   a. Use df(b/w-IV1), df(w/in) and alpha level to find F[crit] for IV1.
   b. Use df(b/w-IV2), df(w/in), and alpha level to find F[crit] for IV2.
   c. Use df(b/w-IV1 x IV2), df(w/in), and alpha level to find F[crit] for IV1 x IV2.
3. Make decisions: See if you have any main effects and/or interaction.

Question 32

Partial eta squared formula

Answer 32

ηp2(x) = SS(b/w-x)/[SS(b/w-total) - SS(b/w-y) - SS(b/w-z)]

Question 33

Partial eta squared definition

Answer 33

Percentage of variance in the DV that can be attributed to the IV, when multiple IVs are present. ONLY calculate for significant results.

Question 34

If the interaction is NOT significant, but main effect(s) are:

Answer 34

2 groups: compare means directly

3+ groups: Run a Tukey or a priori to compare means

Question 35

If the interaction IS significant:

Answer 35

Ignore main effects, as the interaction becomes more interesting to look at statistically. Conduct simple effects.

Question 36

Simple effects definition

Answer 36

Examine the effect of the IV(x) within one level of IV(y). Basically a series of ANOVAs.

Question 37

Simple effects steps

Answer 37

1. Choose direction (horizontal or vertical) in which you will conduct comparisons using the data table. Run comparisons in a way that you are comparing 2 levels to each other so that you don’t have to run a Tukey test if you do get significant results, you can just compare the 2 means to each other with a one-way ANOVA.
2. Complete one-way ANOVA source tables for each level.
   a. Make 3 new source tables, keeping the within values from the two-way ANOVA source table.
   b. Calculate SS(b/w).
   c. Calculate df(b/w).
   d. Calculate MS(b/w).
   e. Calculate F-ratio.
3. Make a decision featuring a Bonferroni correction of the original alpha level.
   a. Divide original alpha level by m (the # of comparisons you are running for the one-way ANOVA)
   b. Round the new alpha level down to use F-ratio table (.10, .05 or .01).
   c. Find new F[crit] value and plot on an F- table graph to make a decision (based on significance)
4. Interpret the meaning of your decision. If it is significant, compare the group means from your IVs to interpret the meaning.

Question 38

SS(b/w) formula for simple effects

Answer 38

SS(b/w) = n(M1 - GM)^2 + n(M2 - GM)^2, where n = # of participants, M1 = mean of IV1, M2 = mean of IV2, and GM = (M1 + M2)/2.

Question 39

df(b/w) formula for simple effects

Answer 39

df(b/w) = k -1

Question 40

MS(b/w) formula for simple effects

Answer 40

MS(b/w) = SS/df

Question 41

F-ratio formula for simple effects

Answer 41

F = MS(b/w)/MS(w/in)