L10 - Two Way between subjects ANOVA

Question 1

What is the main effect in a two-way ANOVA?

Answer 1

A main effect investigates the mean differences between LEVELS OF ONE FACTOR in the two-way design.

Therefore, in a two-way design, there will be TWO main effects - this will correspond to the marginal means of the factor

Question 2

What is the interaction effect?

Answer 2

The interaction effect investigates the differences in the cell means for the two-way factorial classification after the row and column main effects have been removed..

Therefore, an interaction represents differences between levels of one factor at each level of the other factor that are OVER AND ABOVE the differences from the main effects.

Question 3

In a two-way ANOVA, SS total is broken down into SS between and SS within…

What is it further broken down into?

Answer 3

SS between is broken down into

SS between factor a
SS between factor B
SS for interaction

Question 4

Differences between running 3 seperate one way ANOVAS, and a single TWO way ANOVA?

Answer 4

• SSwithin was different for each analysis in 1 way anova, but it was all the same for 2 way anova
• The sum of the three sources of SSbetween in Strategy 2 (i.e. 7696 + 22699 + 3177 = 33572) equals the SS_(S×D) in strategy 1.
• The numerator degrees of freedom for SS(S×D) in strategy 1 (i.e. 5) equals the total of all three numerator degrees of freedom under strategy 2.
• Denominator degrees of freedom vary in strategy 1, whereas they are always the same in strategy 2 (and the same value – 174 – as for sex x diagnosis in strategy 1).

**The Sex x Diagnosis method in Strategy 1 confounds the main effects for sex and diagnosis with the interaction effect, and therefore it does not provide an adequate way to answer RQ3. This is because its numerator degrees of freedom equal 5 and its SS(S×D) value equals the sum of the three SS from strategy 2.

Strategy 2 contains a much more efficient SSwithin value than either of the two values used for the two main effects in Strategy 1. We would therefore expect a greater chance of finding significant results under Strategy 2, because errors are smaller.

Question 5

What are row/column effects?

Answer 5

This is found when you subtract the grand mean from the row/column mean.

Question 6

What are interaction effects?

Answer 6

This is found when grand mean and row and column effects are subtracted from cell mean.

The cell interaction effects sum to zero over rows within each column (i.e. downwards), and over all columns within each row (i.e. across-wise).

Question 7

How do we interpret a plot of the interaction effect in the 2 way anova design?

Answer 7

• A cross over indicates the notion of interaction effects

- you can see interaction effect when the group means don’t follow same trend..?

Question 8

Describe how the 2-way anova is an additive model?

Answer 8

• The model is based on ADDITIVE EFFECTS, in which each raw cell mean is decomposed into 1) row effect, 2) column effect and 3) interaction effect.
• each effect represents some kind of deviation from the grand mean.

Question 9

What is an interaction contrast?

Answer 9

An interaction contrast involves comparing the cell means of the two-way table using the cross-product of contrast weights from the planned comparisons for row effects and the planned comparisons for column effects. The number of interaction contrasts will equal the numerator degrees of freedom for the omnibus interaction F test.

Question 10

What are order zero weights?

Answer 10

when all the weights add up to -1 or +1

Question 11

What are order-1 weights?

Answer 11

When all the weights add up to |2|