Week 5: Repeated-measures ANOVA

Question 1

What is a repeated-measures ANOVA?

Answer 1

It is a within-subjects based ANOVA

- same subjects tested repeatedly hence repeated measures

Question 2

Give some examples of within-subject designs

Answer 2

Subjects get different treatments but the same DV measures (e.g. memory but 3 different memory strategies)

Same subject gets number of different tests - normed with the same scale (intelligence tests)

Same variable measured overtime (depression pre and post treatment)

Multiple DVs measured on the same people (anxiety = DV is measured on paper and other forms of tests following treatment)

Question 3

Advantages to repeated measures design?

Answer 3

Economy of subject number: less people needed

Each subject is their own control: reduces error variance so less unaccounted for noise

Question 4

Disadvantages to repeated measures design?

Answer 4

Order effects: learning or fatigue

Carry-over effects:

Question 5

How do you control order effects?

Answer 5

You can compensate through counterbalancing - smearing the effects equally across conditions

Question 6

Within subjects ANOVAs partition total variance slightly differently. Explain

Answer 6

Between: split into variation due to treatment and then variation due to noise

For within we still have this, but also variation between participants - this means less noise and a smaller error term making it easier to identify significance

Question 7

Repeated or within ANOVAs have a difference with assumptions.. explain

Answer 7

The independence of sampling assumption is obviously violated in a within design. But SPHERICITY is added

Question 8

What is sphericity?

Answer 8

It is the condition where the variances of the differences between all possible pairs of within-subject conditions (i.e., levels of the independent variable) are equal.

Question 9

When is sphericity assumed to be met?

Answer 9

When there are only 2 levels in the IV

Question 10

When do we assume sphericity has been violated?

Answer 10

When you have more than 2 levels

Question 11

How do we test for sphericity?

Answer 11

Mauchlys test

If this is significant - it means that assumption has been violated

Question 12

What do we do if sphericity has been violated?

Answer 12

We can adjust the degrees of freedom within the F equation through a correction factor.

This is a greenhouse-geisser correction that estimates how overly generous the ANOVA is

Question 13

What happens in an ANOVA that has been violated in terms of sphericty?

Answer 13

It becomes overly generous

Question 14

Reporting after you’ve made a greenhouse-geisser correction?

Answer 14

Report the ANOVA F(df,df)= F, p=p

But use values on the GG line instead and state “following a greenhouse-geisser correction”

Question 15

How do you set up repeated-measures ANOVA data in jamovi?

Answer 15

Each level of IV is a separate column

1x row for each participant

Question 16

How do you do a RM ANOVA in jamovi?

Answer 16

ANOVA - Repeated measures
IV - repeated measures factors
Levels - repeated measures cells
DV - DV box

Question 17

Why does jamovi produce a between-subjects table here?

Answer 17

Because this is how within ANOVAs partitions the variation - disregard this table, don’t interpret

Question 18

What do you do if the ANOVA is significant?

Answer 18

Need post hocs to see where differences lie

Bonferonni or Holm - automatically adjust significance value
Tukey or Scheffe may not be valid when sphericity is violated

Question 19

How would you compare baseline and treatment groups?

Answer 19

Compute a new variable from the means of all treatment groups, and another for baseline - you can then perform another RM ANOVA or matched pairs t-tests on these variables

Paired samples t-tests will give cohens d effect sizes

Question 20

What is a limitation of counterbalancing?

Answer 20

You are limited to sample sizes that are multiples of the number of possible orders

Eg. 4 levels = 24, 48, 72, 96

Question 21

Why would we avoid counterbalancing for its larger sample size limitation?

Answer 21

Because it undermines the benefit of having a repeated measures design with less participants

Question 22

What are latin square designs?

Answer 22

They allow a more economical way to counterbalance by instead of using all possible orders, they use a selection of possible orders.

Question 23

Once a latin square is produced, what can you do with it?

Answer 23

Can use it to obtain the sequences for the presentation of treatment conditions to individual participants

But there are also statistical uses

Question 24

What can you statistically do with a latin square design?

Answer 24

The effects of order may be removed from the model by including order - done by including a term for order and making adjustments for differences between means
- provides a more sensitive account of treatment

The error term is the treatment x subjects interaction

Variance is removed from the residual, effectively increasing the F value for the treatment

Question 25

What is a replicated latin square design?

Answer 25

One in which there is more than one occurrence of the same latin square

Question 26

When can’t you control for order effects?

Answer 26

Can only be done if there are no carry over effects as the model assumes no interaction between treatment order and position

Can’t be done with designs with more than 2 levels - because sphericity and order cannot be corrected at the same time

If the order effect is not significant, more appropriate to run the analysis in the repeated measures format to obtain the GG adjustment