repeated and mixed ANOVAs Flashcards
what do repeated ANOVAs allow us to do?
allows us to explain variance that we are yet to be able to explain
what is a One-Way âIndependentâ Samples ANOVA?
- between-subjects
- each participant contributes one data point
- participates in one condition (different people in different conditions)
- subjective to participant effects / differences and variance we cannot account for when using an independent design
how can we account for variance we cannot account for when using an independent design?
Repeated Measures ANOVA
what is a repeated measures ANOVA?
- participants contribute multiple data points (i.e. before and after (counterbalanced) or condition 1 and 2 (two different intervention types)
- same participants are in different conditions
- data points are not independent
what are some benefits of repeated measures?
- Sensitivity
- unsystematic variance is reduced
- more sensitive to experimental effects
- (because unsystematic variance due to individual differences in reduce, the noise in our data is reduced and we are more able to catch an experimental effect which is there)
- economy -> fewer participants needed
what is the theory of ANOVAs?
if group (IVs) are truly different (shown in DV) then MSm > MSr
* model explains a large proportion of the variance
In repeated measures, what variance are we explaining?
within-subject variance (everything within our experiment or other within subject factors)
* between-subject is the residual variance (stuff that cannot be explained while using our model) -> we ignore the variance between individuals
what does the F statistic look at?
variance explained by the model (/) as explained as the variance is left over
F =
MSm / MSr
MSm
Variance explained by model (âsystematic varianceâ)
MSr
variance leftover (noise)
what are some problems with repeated measures?
- same participants in all conditions means scores across all conditions correlate with each other -> violating assumptions of sphericity
i.e. high scores in condition 1 should also be higher scorers in condition 2
how are problems with correlating scores understood?
sphericity -> so a standard ANOVA assumes the correlation between those conditions is the same across combinations or âvariances in the differences between conditions are equal
what does sphericity rely on?
people are internally consistent -> if this doesnât happen, it distributes sphericity
how is sphericity measured?
Mauchlyâs Test
Mauchlyâs Test
- only applies when there are within subject factors
we expect the difference that the correlations between each of the different combinations of conditions to be roughly equal -> so we expect there not to be a massive difference between scores
when is sphericity violated?
P < .05 (P is smaller than .05 -> p is significant)
when is sphericity met?
P > .05 (P is greater than .05 -> p is non-significant)
when does sphericity apply?
when you have more than two levels of IV
* if you run Mauchlyâs test on a variable with only 2 levels, youâll get black outputs
how do we fix deviations of sphericity (other assumptions are met)
- âIndependence = Maximum Freedomâ
â Independence -> more variance
â Repeated measures -> less variance
Therefore, we must manually correct the degrees of freedom in our model (multiplying it by a âcorrection factorâ but SPSS does this for us)
how estimates of sphericity can be multiple by?
- Greenhouse-Geisser Estimate
- Huynh-Feldt Estimate
- Lower Bound
Greenhouse-Geisser Estimate
conservative; constrains the independence and violations/accounts for sphericity
Huynh-Feldt Estimate
liberal; more likely to find a significant result than GGE
Lower Bound
Most extreme correction; unlikely to give significant results
what does multiplying degrees of freedom by estimates of sphericity do for violations of sphericity?
- Corrections for the violation of sphericity making it less likely that
- It takes correlation factors that are calculated based on how much you violated sphericity and multiplied each of the degrees of freedom by that and correcting the p value as such
REALLY IMPORTANT TO CHECK P-VALUE BECAUSE YOU MAY NEED TO LOOK AT OTHER THINGS
* still has error degrees of freedom
if there are 2 levels Time (Before and After) and contrast (7 Levels). What do you call this design?
2 x 7 Repeated Measures ANOVA
what may we see if thereâs a big difference in contrasts?
an interaction effect
* higher contrast it has an effect, whereas at lower contrast it doesnât
how do you organise the data for SPSS?
- One row per participant
- One column per condition (i.e. so 2x7 ANOVA would have 14 columns)
- No need for coding variables (e.g. 1 = 1 condition 1 etc.)
How to run repeated measures ANOVA in SPSS?
- Analyse > General Linear Model > Repeated Measures
- The box will ask you to define your repeated measures factors (but only your within subject factors) -> Type in the factor name and Type in the number of levels (i.e. 2 and 7)
- Name your dependent variable (optional) -> Alex says not to do this!
- Drag data into factors
â This tells SPSS which column match up with the variables you have just defined
â Make sure you get these the right way around
â EXPECTED YOU TO PUT THE VARIABLES IN TIME (2) AND THEN CONTRAST (7)
â ASKING FOR THEM IN A SPECIFIC ORDER -> i.e. wants level 1 of variable 1 and level 1 of variable 2 AND then the first level of time and then the second level of the second variable AND then level 1 of variable 1 and level 3 of variable 2 AND then 2,1 = second level of first variable and the first level of the second variable - Click Block ( most levels on the horizontal axis) > Add > Continue
- Might want to put a contrast: contrast > compare each contrast with the baseline (first condition) using simple contrast
â No contrast for time because it only has two levels- the main effect tells you everything you need - Post Hoc Tests: Drag your factors and interactions to Displays Mean for box (> compare main effects: Bonferroni) > Descriptives, Effective Sizes & Power, Homogeneity
â No need to run post hoc and contrasts - RUN THE TEST
Understanding the Output:
- check the factors (they are in the right place) and variables match up
- check means and N in the descriptive statistics table
- graphs will appear at the bottom and they are a good idea to check first (allows you to see if the data is sensible)
- multivariate tests -> this table is the first thing you will see but we usually ignore it as these are not ANOVA results (USED AS an alternative to the ANOVA if assumptions are violated, any other type of normality)
Understanding the Outputs (Mauchleyâs Test of Sphericity)
- W statistics and p values are all IVs and interactions (more than two levels)
P < .05 (less than) -> sphericity violated and we will have to reported correction values later
(if in doubt, GHG correlation is the best use)
Understanding the Outputs: Main ANOVA Table
- Test of Within-Subject Effects TABLE!!
- F ratios and p values for each main effect and interactions
- For df, youâd go along and do (the normal df, the error df for each condition)
- If Sphericity is violated, report from the corrected rows
- F(df1, df2)=, p= [for each effect/interaction]
Questions to ask yourself in a Repeated Measures ANOVA?
What is the significant main affect of âŚ
Significant effect of âŚ
Significant interaction betweenâŚ
Writing up repeated measure ANOVA:
- Report F (df1, df2) and p for each main effect and any interaction effects
- contrast or post-hoc tests can be reported in table or in text
- remember to think about interactions in your discussion -> donât just focus on main effects
what is a mixed ANOVA?
within and between subject variance is explainable
* total variance split into between and within variance
For mixed ANOVA, you may have:
- between-subject factors
- different subjects in each substance group, and there were all still tested at all contrast levels at both times
- still a DV
How to set up the data for a mixed ANOVA?
- set up data as you did for repeated measures
- need a coding variable for each between-subject factor
- one row per participant
- one column for coding between subject factors
- one column per repeated measure condition
Running the ANOVA:
- Analyse > general linear model > repeated measures (set up factors as you would for repeated) and put the factor in the between-subject factors (if thereâs more than one, stick it in there as well)
- Set up the data as you would before
- EVERYTHING YOU SHOULD LOOK FAMILIAR IN THE OUTPUT
- Test of Between-Subject Effects will just have the main affect of the IVs in (will tell you no difference between those in each condition)
- Test of Within-Subject Effects:
- Will show you any contrasts i.e. three way reactions
- We have our combinations of variables
- We are particular interested in how time and contrast interact with substance (for example)
THEN WE HAVE TO FIGURE OUT WHAT THIS MEANS)
ANOVAs will give us _ _ each IV but also _ _
main effects, two-way interactions
some types of interactions we may see
- C1 * C2
- C2 * C3
- C2 * C3
- C1 * C2 * C3
