ANOVA lecture 12 Mixed designs

Question 1

Mixed design

Answer 1

Experiments with one between-subjects variable, and one within-subjects (repeated measures) variable
(e.g. A bit difficult to manipulate males and females in the same person for example.)

These experiments will have J different groups of subjects, with subjects in each group being repeatedly measured on the same DV under (K) different conditions
J x (K) 

For the 2 x (3) you have one between subjects variable with j=2 levels and one within subject variable with k=3 levels.

Question 2

whats a 3 X (3) mixed design

Answer 2

IVA has three levels, IVB has three levels as well. Type of therapy and time follow up.

Question 3

2 x 3 between-subjects factorial design

Answer 3

different groups of participants tested among all six groups. Each participant or each person is only exposed to one JxK on the DV.
The DV effect could be due to effects or individual differences. Potential internal validity.

Question 4

(2 x 3) within-subjects factorial design

Answer 4

Both numbers are in brackets so all within.
Changes on the DV can be identified across each jxK conditions, so you create a difference/change/contrast score for each person.

Problem: you must test for a longer period, also order effects (counterbalancing necessary)

Question 5

why do you make contrast in J x K layout even for the two IV contrast?

Answer 5

you need to make the JxK layout before you can make the interaction contrasts eg everybody getting therapy gets a one.
(Notice that if you flip the variables around, so kxJ instead of jxk, the variables will be different.)

Question 6

HOw to interpret interaction question

2 -1 -1 2 -1 -1 -4 2 2

Answer 6

Is the difference between 2 ans -1 (first two contrast three sets) different to the difference between 4 and -2 (the third set of three numbers.
Circle the numbers first so (2 -1 -1) ((2 -1 -1) (-4 2 2)

Question 7

what do we think when we see TEsts of within subjects effects written in SPSS

Answer 7

It’s the omnibus anova, NOT THE CONTRAST -> no direction

Question 8

does spss use seperate error terms for mixed designs?

Answer 8

yes. each variable has it’s own.

Question 9

for between subject variable in a mixed design, what error term is used?

Answer 9

Both the A1 and A2 (between-subjects) main effect contrasts are tested use the same error term from

Question 10

what happens if orthogonal and normalised contrasts in mixed designs

Answer 10

Sum of the SS will add up to SS(Error) because the contrasts are orthogonal, and all of the SS have been normalised. This is because the experiementer has tested k-1 mutually orthogonal contrasts. The SSs partition.

Question 11

what error for mixed designs for product interatcions?

Answer 11

Product interactions involving a between-subjects variable and a within-subjects variable are always tested using the same error term as the within-subjects variable

Because this is based on variablity in scores we cannot account for after removing the main effect of A, B and after removing overall differences between participants (S bar i). It’s the bit we really cannot account for.

Question 12

what is v2 for mixed design contrasts?

Answer 12

Suppose the researcher wished to control the FER at .05, using bonferroni, it’s J(n-1) or the error df for each contrast. SEPERATE ERROR FOR EACH FAMILY
dfW for contrasts is the same as mixed designs as it is for within subjects designs. But you can read it straight out of the output.

Question 13

how do you find the main effects of A1 and A2 contrasts?

Answer 13

Look at the row means to interpret the A1 and A2 main effect contrasts.

Question 14

how do you draw interaction conclusions for mixed designs?

Answer 14

You start with a 3x(3) grid of the cell means. But we need to collapse it into a 2x2 grid.

1) find whats in the A1B1 contrast into a grid
2. A1B2
3. A2B1
4. A2B2

Look at the mini grid for just A1B1 (see the numbers as a line plot. Do the lines cross over? PARALLEL? Then interpret if this difference is different to that difference

Question 15

how to write the non sig interaction between time and therapy?

Answer 15

the lack of difference between post therapy and follow up (dotted line vs straight line), the difference is not different from that difference at cog and beh therpay

Question 16

Another way of testing contrasts for mixed designs

Answer 16

one sample t test. For purely within subject designs there is one group of participants. (using row means and column means)
For mixed designs we can have multiple groups of people.
We could have also used a between subjects ANOVA for the A and B contrast, and another between subjects ANOVA for the others, if we also then compute contrasts ourselves.

Question 17

how would you do a main effect contrast for t tests>

Answer 17

Compute wellbeing scores for each participant averaged over time of assessment [meanT = (pre+post+follow)/3]
These numbers are the row means from the 3x3 grid. Once you’ve done pre averaging, you can put them into a between subjects anova with DV wellbeing, IV as therapy

Question 18

Group differences on contrast scores for t test anova mixed design contrasts?
what is intercept in spss output?

Answer 18

Main effect: Does the ‘grand mean’ differ significantly from 0? Does the mean of YcB1 differ significantly from 0? Do changes in wellbeing from before to after differ significantly from 0 (averaged over therapy type)?
We are testing whether There is no sig diffference across the enture column of YcB1 scores. No change from post to follow up

Test of the intercept is the main effect contrast B1.

Int effect: look at custom hypothesis tests, it will say Dependent variable YcB2 etc at the top of a box. That’s your contrast