Repeated measures ANOVA

Question 1

How many IV levels are needed to have issues with sphericity?

Answer 1

3 or more

Question 2

Can Mauchley’s test of sphericity be used to assess compound symmetry?

Answer 2

Yes, but sphericity is a relaxed version of compound symmetry.

Question 3

What does a significant Mauchley’s test reveal?

Answer 3

There is a significant violation of assumptions about sphericity

Question 4

What are the consequences for lacking homogeneity of variance in between groups ANOVA and lacking sphericity in within participants ANOVA?

Answer 4

Type 1 error bias, making it more likely to get significant results that are not real.

Question 5

When should we apply the Greenhouse-geisser epsilon adjustment?

Answer 5

Always apply the correction to be safe, as Mauchley’s test is not robust and often ignored all together.

Question 6

Why is greenhouse-geisser epsilon adjustment most recommended?

Answer 6

The adjust it gives is proportional to the violation of sphericity observed.

Question 7

What do higher epsilon values represent? Lower values?

Answer 7

Closer to 0 = larger adjustment to compensate (to be more conservative) greater sphericity violation
Closer to 1 = less adjustment

Question 8

How do we overcome the fact that repeated measures designs violate the assumption of independent scores in ANOVA?

Answer 8

Participants are treated as a factor, which is cross with the focal IV

Question 9

In a within-participants ANOVA, what does between participants variance (aka individual differences) get removed from?

Answer 9

Both the error and the treatment effect

Question 10

What makes up the F test in WP ANOVA?

Answer 10

The treatment effect / (treatment x participants effect)

Question 11

Why does the treatment x participants interaction serve as the error in WP ANOVA?

Answer 11

The interaction is the variance in the DV which is not attributable to any main effects alone. Because we want to remove the effect of participants (IV1), by design, and don’t want to consider the treatment variance again (IV2), the interaction (I.e. remaining variance) is an appropriate error term which excludes the effects of these two things.

Question 12

How do we frame error within a repeated measures ANOVA? What does this imply about the generality of error throughout the model?

Answer 12

Inconsistencies in the effect of the focal IV across participants. The error depends on the participants and treatment in focus; therefore cannot use pooled error terms for all tests.

Question 13

What is a fixed a factor?

Answer 13

Where either all levels of the IV have been sampled, or particular levels selected for theoretical reasons.

Question 14

What is a random factor?

Answer 14

A IV/factor where levels are chosen at random.

Question 15

Two requirements for compound symmetry?

Answer 15

1. Homogeneity of variance (diagonal matrix values)

2. Homogeneity of covariances

Question 16

When do we require the assumption of compound symmetry to be met?

Answer 16

When using a random factor

Question 17

Which is the best multivariate test to use?

Answer 17

Wilks’ Lambda

Question 18

What are disadvantages of within-participants design? (2)

Answer 18

1. Restrictive statistical assumptions

2. Confounds due to sequencing effects in the study

Question 19

Why is counterbalancing not a magical solution to order effects? (2)

Answer 19

1. Carry-over effects still inflate error (although unsystematically due to random assignment to counter balance condition)
2. There can still be treatment x order interactions

Question 20

What is the error term for every test in a RM ANOVA?

Answer 20

It is always the effect x participants interaction