Repeated-Measures designs: Mixed Models Flashcards
What is a repeated-measures design?
Each participant contributes more than one data point
In an experimental design, participants take part in more than one condition
What type of stats test would we use for repeated-measures designs?
Mixed models (aka hierarchical/multilevel modelling)
Why would you use a Mixed Model for a repeated-measures design rather than a repeated-measures ANOVA?
Sphericity is less of an issue
Better able to handle missing values
Can treat time as a continuous variable (where repeated-measures ANOVA can only treat it as categorical)
What are the practical differences with how data needs to be presented in Mixed-Model in Jamovi (compared to an ANOVA)
Normally you’d present data with each row representing a participant and several (DV) observations next to that participant in that row
In a mixed model, each row represents an observation (on a DV) instead - as seen in attached image
What are your analysis options for the following design?
Q - does students’ alcohol consumption change over the course of a term
H - alcohol consumption will be lower later in a term
DV - self-reported alcohol consumption
IV - two time points (which the DV is measured at): week 2/time 1, and week 9/time 2
paired-samples t-test
OR
one-way mixed model
What are your analysis options for the following design?
Q - does students’ alcohol consumption change over the course of a term
H - alcohol consumption will be lower later in a term, compared to early in and midway through a term
DV - self-reported alcohol consumption
IV - three time points (which the DV is measured at): time 1, time 2 and time 3
one-way mixed model is the only option
- allows an overall test of differences over time
- allows tests of specific comparisons between individual time points and specific trends across time points
In Jamovi, when looking at factors coding for a One-Way Mixed Model - what is the difference between polynomial coding and difference coding (as can be selected in a dropdown)
Polynomial coding gives linear and quadratic contrasts (and more if there are more than 3 levels)
Difference coding asks for contrasts between Time 3, and Time 1 & 2 combined
And for contrasts between Time 1 and Time 2, ignoring Time 3
Here is the first part of an output from a One-Way Mixed Model - what does this tell us
The main effect of time is highly significant
Here is the second part of an output from a One-Way Mixed Model (polynomial coding) - what does this tell us
There is a significant linear trend
But not a significant quadratic trend
Here is the third part of an output from a One-Way Mixed Model (difference coding) - what does this tell us
Both ‘special’ contrasts (T1&T2 vs T3, T1 vs T2) are significant
What questions need to be considered to determine if a study has a Mixed design when there is more than one IV
If both IVs are repeated measures (Ps take part in all conditions/at each time/complete all measures) then it’s not a mixed design
If one of the IVs is between-participants (each participant takes part in one condition only) then the study has a mixed design
What are the independent variables for the following design?
Q - does students’ alcohol consumption affect performance on hand-eye coordination tasks
H - alcohol consumption will reduce performance on hand-eye co-ordination tasks, BUT only for difficult tasks and not for easy tasks
DV - performance on hand-eye coordination tasks
M - each participant attempts the hard and easy tasks without consuming alcohol, then does them again after consuming alcohol OR vice versa (why is this?)
How does an interaction effect relate to this?
IV1 = alcohol consumption (control vs alcohol), repeated measures
IV2 = task difficulty (easy vs difficult), repeated measures
Vice-versa is to counterbalance the order of conditions (avoid order effects)
The effect of IV1 depends on IV2 - an interaction effect
What are your analysis options for the following design?
Q - does students’ alcohol consumption affect performance on hand-eye coordination tasks
H - alcohol consumption will reduce performance on hand-eye co-ordination tasks, BUT only for difficult tasks and not for easy tasks
DV - performance on hand-eye coordination tasks
IV - alcohol consumption (have or haven’t consumed)
- task difficulty (hard or easy)
Two-Way Mixed Model
- tests the main effects of the two IVs (effect of alcohol collapsed across task difficulty and vice versa)
- tests the interaction between the two IVs (extent to which effect of alcohol varies depending on task difficulty)
Simple Main Effects Analysis also needed
- tests the main effect of IV1 (alcohol) at each different level of IV2 (task difficulty)
This is an output from a Two-Way Mixed Model - what does it tell us?
Main effects of alcohol and task difficulty are both significant
The interaction between alcohol and task difficulty is also significant
This is an output from a Simple Main Effects Analysis - what does it tell us
The simple main effect isn’t significant in the easy task condition
But it is significant in the hard task condition
This is the output of a Three-Way Mixed Model - what does it tell us?
Both alcohol and task difficulty have significant main effects
There’s a significant two-way interaction between alcohol & task difficulty
The 3-way interaction is non-significant
SO alcohol consumption reduced performance on hand-eye coordination tasks but only for difficult tasks (this is a two-way interaction between alcohol and task difficulty)
and this didn’t depend on if participants played sports (non-sig three-way interaction)
This is the output of a Simple Main Effects Analysis of a Three-Way Mixed Model - what does it tell us?
The simple main effect of alcohol is only siginificant in the hard task condition for people who don’t play sports
But if the 3-way interaction effect is shown to be non-significant in the previous analysis then this effect we’ve just found isn’t significantly different from the effect in other conditions
