Complex Within subjects ANOVA

Question 1

complex repeated measures design

Answer 1

• All participants contribute a score to each condition
  
  • As we add more IVs, the number of total conditions multiplies
    ○ 1 IV with 3 levels: each person contributes to 3 conditions
    ○ 3 IVs, each with 3 levels: each person contributes to 333 = 27 conditions!!
  • The key limitations of complex repeated measures designs is that we need to test every participant a lot of times!
  • Potential “order effects” can complicate our ability to make robust inferences

Question 2

carry over effects

Answer 2

• This is where one condition “bleeds” into another
• For example, imagine we got our participants to do the high stress, medium stress and control conditions on the same day.
• A participants who does high stress followed by control, is likely to be still stressed when they do the control condition (even with a few hours gap)
• Someone who does control then stress will have no carry over.
• Doesn’t have to be a something obvious like a major stressor, pharmacological intervention etc.
  This even occurs in the most basic cognitive tasks

Question 3

how to deal with carry over effects

Answer 3

(1) Trying to make the carry over effects equal between conditions
* If possible, randomizing conditions between trials or blocks
* Using counterbalancing and other forms of condition order randomization (we’ll go into more detail on this soon)
- (2) Accounting for carry over effects in the statistical analysis
* For example, including this information as another variable in an ANOVA
* Essentially, trying to make sure that any carry over effects are not incorrectly attributed to the IVs of interest

Question 4

practice effects

Answer 4

• People get better at tasks with more practice, which can happen for many reasons
• The cognitive processes that underpins tasks can change with practice:
  
  • If the same or very similar questions are repeated, the memory retrieval process may take over from the process used to solve the question
• People may develop strategies to improve performance:
  
  • You can be quicker overall in a Stroop task by defocusing to ignore the word
• Some tasks have a rule that can be learnt, which changes performance:
  In the Iowa gambling task, most people learn that low risk low pay off decks are better than high risk high pay off decks

Question 5

how to deal with practice effects

Answer 5

• (1) Giving people time to achieve “peak performance”
  
  • For example, practice trials or blocks (or sessions…) to get them used to the task and ignore those blocks to have stable performance
• (2) Trying to make the practice effects equal between conditions
  
  • If possible, randomizing conditions between trials or blocks, instead of doing one entire condition before another entire condition
  • If not possible, having different sessions for different conditions, which are far enough apart (e.g., a week) that practice effects have hopefully disappeared

Question 6

fatigue effects

Answer 6

• People can get worse at tasks if they spend too long on them
  
  • For example, lecturers can get worse at making lecture slides the longer they spend making lecture slides, and these slides can get increasingly boring…
• Often an issue in long studies with a large number of trials or items
  
  • More conditions usually means more trials, so studies with lots of repeated measures can be very tiring
    This can also cause attrition issues, where people fail to complete the study

Question 7

how to deal with fatigue effects

Answer 7

• (1) Giving people adequate breaks
  
  • For example, breaks between blocks of trials
  • Splitting longer experiments into multiple sessions to reduce fatigue
    (2) Trying to make the practice effects equal between conditions
    If possible, randomizing conditions between trials or blocks, instead of doing one entire condition before another entire conditions
    If not possible, having different sessions for different conditions

Question 8

counterbalancing

Answer 8

• Imagine we wanted to look at the effect of a stress manipulation on social interaction, and decide to compare a stress condition to a no stress condition. Participants could be split up into two separate (typically equal) “groups” who each do the conditions in a different order:
• However, this starts to become difficult if we add more and more conditions. If we added a mild stress condition
• 3 levels of the IV means 6 possible orders are available. Participants would be randomly assigned to these groups
  However, what about an experiment with 4 levels of the IV? This keeps expanding…

Question 9

latin square design

Answer 9

• In an experiment with four conditions there are 24 orders
• Latin squares are used as there are too many orders to effectively counterbalance
• In an experiment with four conditions there are 24 orders
• Latin squares are used as there are too many orders to effectively counterbalance
• Each condition precedes and follows each other condition once and once only

Question 10

repeated measures designs

Answer 10

• Repeated Measures (within subjects) designs have key advantages
  
  • Control for individual differences in participants
  • Need less participants (increased power)
• However, there are a range of potential order effects that can occur when testing people multiple times, which can invalidate our inferences if not properly dealt with
  Careful consideration of optimal experimental design is needed

Question 11

what to do in R

Answer 11

1. install and download packages
2. load and look at the data
3. test assumptions (normality)
4. run the ANOVA
5. run post hoc tests (pairwise comparisons and bonferroni)

Question 12

summary

Answer 12

• “Complex” designs, in this context, refer to designs with 2 or more Ivs
• Complex Repeated Measures Designs are usefully for creating a powerful test
• However, they also create a potential for confounding order effects
• Complex “ANOVAs” (Linear Mixed Models) have “main effects” and interactions
• Main effects are the effect of an IV averaged over the other Ivs
• Interactions are where the effect of one IV on the DV is dependent on another IV
• Alone, the interaction tells us only that a dependency exists. We have to break down the interaction (usually with post-hoc tests) to understand what the dependency is.