repeated and mixed ANOVAs

Question 1

what do repeated ANOVAs allow us to do?

Answer 1

allows us to explain variance that we are yet to be able to explain

Question 2

what is a One-Way ‘Independent’ Samples ANOVA?

Answer 2

• 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

Question 3

how can we account for variance we cannot account for when using an independent design?

Answer 3

Repeated Measures ANOVA

Question 4

what is a repeated measures ANOVA?

Answer 4

• 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

Question 5

what are some benefits of repeated measures?

Answer 5

• 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

Question 6

what is the theory of ANOVAs?

Answer 6

if group (IVs) are truly different (shown in DV) then MSm > MSr
* model explains a large proportion of the variance

Question 7

In repeated measures, what variance are we explaining?

Answer 7

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

Question 8

what does the F statistic look at?

Answer 8

variance explained by the model (/) as explained as the variance is left over

Question 9

F =

Answer 9

MSm / MSr

Question 10

MSm

Answer 10

Variance explained by model (‘systematic variance’)

Question 11

MSr

Answer 11

variance leftover (noise)

Question 12

what are some problems with repeated measures?

Answer 12

• 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

Question 13

how are problems with correlating scores understood?

Answer 13

sphericity -> so a standard ANOVA assumes the correlation between those conditions is the same across combinations or ‘variances in the differences between conditions are equal

Question 14

what does sphericity rely on?

Answer 14

people are internally consistent -> if this doesn’t happen, it distributes sphericity

Question 15

how is sphericity measured?

Answer 15

Mauchly’s Test

Question 16

Mauchly’s Test

Answer 16

• 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

Question 17

when is sphericity violated?

Answer 17

P < .05 (P is smaller than .05 -> p is significant)

Question 18

when is sphericity met?

Answer 18

P > .05 (P is greater than .05 -> p is non-significant)

Question 19

when does sphericity apply?

Answer 19

when you have more than two levels of IV
* if you run Mauchly’s test on a variable with only 2 levels, you’ll get black outputs

Question 20

how do we fix deviations of sphericity (other assumptions are met)

Answer 20

• “Independence = Maximum Freedom”
  ○ Independence -> more variance
  ○ Repeated measures -> less variance
  Therefore, we must manually correct the degrees of freedom in our model (multiplying it by a ‘correction factor’ but SPSS does this for us)

Question 21

how estimates of sphericity can be multiple by?

Answer 21

• Greenhouse-Geisser Estimate
• Huynh-Feldt Estimate
• Lower Bound

Question 22

Greenhouse-Geisser Estimate

Answer 22

conservative; constrains the independence and violations/accounts for sphericity

Question 23

Huynh-Feldt Estimate

Answer 23

liberal; more likely to find a significant result than GGE

Question 24

Lower Bound

Answer 24

Most extreme correction; unlikely to give significant results

Question 25

what does multiplying degrees of freedom by estimates of sphericity do for violations of sphericity?

Answer 25

* 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

Question 26

if there are 2 levels Time (Before and After) and contrast (7 Levels). What do you call this design?

Answer 26

2 x 7 Repeated Measures ANOVA

Question 27

what may we see if there's a big difference in contrasts?

Answer 27

an interaction effect * higher contrast it has an effect, whereas at lower contrast it doesn't

Question 28

how do you organise the data for SPSS?

Answer 28

* 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.)

Question 29

How to run repeated measures ANOVA in SPSS?

Answer 29

1. Analyse > General Linear Model > Repeated Measures 2. 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) 3. Name your dependent variable (optional) -> Alex says not to do this! 4. Drag data into factors ○ This tells SPSS which column match up with the variables you have just defined ○ Make sure you get these the right way around ○ EXPECTED YOU TO PUT THE VARIABLES IN TIME (2) AND THEN CONTRAST (7) ○ 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 5. Click Block ( most levels on the horizontal axis) > Add > Continue 6. Might want to put a contrast: contrast > compare each contrast with the baseline (first condition) using simple contrast ○ No contrast for time because it only has two levels- the main effect tells you everything you need 7. Post Hoc Tests: Drag your factors and interactions to Displays Mean for box (> compare main effects: Bonferroni) > Descriptives, Effective Sizes & Power, Homogeneity ○ No need to run post hoc and contrasts 8. RUN THE TEST

Question 30

Understanding the Output:

Answer 30

* 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)

Question 31

Understanding the Outputs (Mauchley's Test of Sphericity)

Answer 31

* 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)

Question 32

Understanding the Outputs: Main ANOVA Table

Answer 32

* Test of Within-Subject Effects TABLE!! * F ratios and p values for each main effect and interactions * For df, you'd 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]

Question 33

Questions to ask yourself in a Repeated Measures ANOVA?

Answer 33

What is the significant main affect of … Significant effect of … Significant interaction between…

Question 34

Writing up repeated measure ANOVA:

Answer 34

* 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 -> don't just focus on main effects

Question 35

what is a mixed ANOVA?

Answer 35

within and between subject variance is explainable * total variance split into between and within variance

Question 36

For mixed ANOVA, you may have:

Answer 36

* 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

Question 37

How to set up the data for a mixed ANOVA?

Answer 37

* 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

Question 38

Running the ANOVA:

Answer 38

1. Analyse > general linear model > repeated measures (set up factors as you would for repeated) and put the factor in the between-subject factors (if there's more than one, stick it in there as well) 2. Set up the data as you would before 3. EVERYTHING YOU SHOULD LOOK FAMILIAR IN THE OUTPUT 4. 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) 5. 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)

Question 39

ANOVAs will give us _ _ each IV but also _ _

Answer 39

main effects, two-way interactions

Question 40

some types of interactions we may see

Answer 40

* C1 * C2 * C2 * C3 * C2 * C3 * C1 * C2 * C3