Week 5: Repeated-measures ANOVA Flashcards
What is a repeated-measures ANOVA?
It is a within-subjects based ANOVA
- same subjects tested repeatedly hence repeated measures
Give some examples of within-subject designs
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)
Advantages to repeated measures design?
Economy of subject number: less people needed
Each subject is their own control: reduces error variance so less unaccounted for noise
Disadvantages to repeated measures design?
Order effects: learning or fatigue
Carry-over effects:
How do you control order effects?
You can compensate through counterbalancing - smearing the effects equally across conditions
Within subjects ANOVAs partition total variance slightly differently. Explain
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
Repeated or within ANOVAs have a difference with assumptions.. explain
The independence of sampling assumption is obviously violated in a within design. But SPHERICITY is added
What is sphericity?
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.
When is sphericity assumed to be met?
When there are only 2 levels in the IV
When do we assume sphericity has been violated?
When you have more than 2 levels
How do we test for sphericity?
Mauchlys test
If this is significant - it means that assumption has been violated
What do we do if sphericity has been violated?
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
What happens in an ANOVA that has been violated in terms of sphericty?
It becomes overly generous
Reporting after you’ve made a greenhouse-geisser correction?
Report the ANOVA F(df,df)= F, p=p
But use values on the GG line instead and state “following a greenhouse-geisser correction”
How do you set up repeated-measures ANOVA data in jamovi?
Each level of IV is a separate column
1x row for each participant
How do you do a RM ANOVA in jamovi?
ANOVA - Repeated measures
IV - repeated measures factors
Levels - repeated measures cells
DV - DV box
Why does jamovi produce a between-subjects table here?
Because this is how within ANOVAs partitions the variation - disregard this table, don’t interpret
What do you do if the ANOVA is significant?
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
How would you compare baseline and treatment groups?
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
What is a limitation of counterbalancing?
You are limited to sample sizes that are multiples of the number of possible orders
Eg. 4 levels = 24, 48, 72, 96
Why would we avoid counterbalancing for its larger sample size limitation?
Because it undermines the benefit of having a repeated measures design with less participants
What are latin square designs?
They allow a more economical way to counterbalance by instead of using all possible orders, they use a selection of possible orders.
Once a latin square is produced, what can you do with it?
Can use it to obtain the sequences for the presentation of treatment conditions to individual participants
But there are also statistical uses
What can you statistically do with a latin square design?
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
What is a replicated latin square design?
One in which there is more than one occurrence of the same latin square
When can’t you control for order effects?
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
