Within subjects ANOVA

Question 1

Repeated measures is synonymous with

Answer 1

Within subjects

Question 2

The main advantage of the within subjects design is

Answer 2

• that it controls for individual differences between participants.
• In between groups designs some fluctuation in the scores of the groups that is due to different participants providing scores
• To control this unwanted variability participants provide scores for each of the treatment levels
• The variability due to the participants is assumed not to vary across the treatment levels

Question 3

Analysis of variance can handle both

Answer 3

Between groups and within subjects

•groups of participants all completing each level of the treatment variable

Question 4

Disadvantages of within subjects design

Answer 4

• Practice Effects
• Participants may improve simply through the effect of practice on providing scores.
• Participants may become tired or bored and their performance may deteriorate as the provide the scores.
• Differential Carry-Over Effects
• The provision of a single score at one treatment level may positively influence a score at a second treatment level and simultaneously negatively influence a score at a third treatment level
• Data not completely independent (assumption of ANOVA)
• Sphericity assumption (more later)
• Not always possible (e.g. comparing men vs women)

Question 5

What are practise effects?

Answer 5

• Participants may improve simply through the effect of practice on providing scores.
• Participants may become tired or bored and their performance may deteriorate as the provide the scores.

Question 6

What are differential carry-over effects?

Answer 6

The provision of a single score at one treatment level may positively influence a score at a second treatment level and simultaneously negatively influence a score at a third treatment level

Question 7

•We can partition the basic deviation between the individual score and the grand mean of the experiment into two components

Answer 7

• Between Treatment Component - measures effect plus error

* Within Treatment Component - measures error alone

Question 8

AS-T

Answer 8

Is the basic deviation

Question 9

AS-A

Answer 9

is the within treatment deviation

Question 10

A-T

Answer 10

Is the between treatment deviation

Question 11

The within treatment component

Answer 11

AS-A

• estimates the error
• At least some of that error is individual differences error, i.e., at least some of that error can be explained by the subject variability
• In a repeated measures design we have a measure of subject variability S-T

Question 12

•If we subtract the effect of subject variability away from the within treatment component

Answer 12

(AS-A) - (S-T)

Question 13

If we subtract the effect of subject variability away from the within treatment component

We are left with a more …

Answer 13

• representative measure of experimental error
• This error is known as the residual
• The residual error is an interaction between
• The Treatment Variable
• The Subject Variable

Question 14

•The residual error is an interaction between…

Answer 14

• The Treatment Variable

* The Subject Variable

Question 15

Mean square estimates of variability are obtained by…

Answer 15

•dividing the sums of squares by their respective degrees of freedom

Question 16

We can calculate F-ratios for both the

Answer 16

main effect and the subject variables

Question 17

Analytical comparisons

Answer 17

• As with a one-way between groups analysis of variance a significant main effect means
• There is a significant difference between at least one pair of means
• A significant main effect doesn’t say where that difference lies
• We can use planned and unplanned (post hoc) comparisons to identify where the differences are

Question 18

A significant main effect of the subject variable is

Answer 18

common and usually is not a problem

Question 19

A significant main effect of the subject variable is

Answer 19

A problem
•when specific predictions are made about performance
•when there is a hidden aptitude treatment interaction

Question 20

There are two possible ways to partition the variability in a two-way repeated measures design

Answer 20

•Construct an overall error term for all the effects of interest
We may overestimate the error for some individual effects
Ignore an additional assumption made in repeated measures designs
Homogeneity of Difference Variances Assumption

•Construct an error term for each of the effects of interest
We will never overestimate the error
We can temporarily ignore the homogeneity of difference variance assumption

Question 21

Error terms in a two way within subjects design

Answer 21

• The error terms for the main effects are the residual for each main effects.
• The error term for the interaction is based on the interaction between the two independent variables and the subject variable

Each effect has a different error term in a within subjects design

Question 22

Testing the main effects and the interaction is done by

Answer 22

As in all other ANOVAs the effects are tested by constructing F-ratios

Question 23

Planned comparisons can be conducted on

Answer 23

Main effects and interactions

Question 24

•Significant main effects can be further analysed using

Answer 24

Appropriate post Hoc tests

Question 25

When analysing significant interactions…

Answer 25

simple main effects analysis can be conducted

If there is a significant simple main effect with more than two levels then the appropriate post hoc tests can be used to further analyse these data

Question 26

ANOVA makes several assumptions

4

Answer 26

• Data from interval or ratio scale (continuous)
• Normal distributions
• Independence
• Homogeneity of variance

Question 27

•Within subjects ANOVA adds another assumption

Answer 27

• ‘Sphericity’: homogeneity of treatment difference variances
• Sphericity is a special case of ‘compound symmetry’, so some people use this term
• There is no need to test for sphericity if each IV has only two levels

Question 28

SPSS provides a test of sphericity called

Answer 28

Mauchly’s test of sphericity

• If it is not significant then we assume homogeneity of difference variances
• If it is significant then we cannot assume homogeneity of difference variances
• If we do not correct for violations, ANOVA becomes too liberal
• We will increase our rate of type 1 errors

Question 29

SPSS provides alternative tests when…

Answer 29

sphericity assumption has not been met