Lecture 8: Research Questions for Group Differences III (Within-subjects for 3+ groups)

Question 1

What constitutes dependent groups analyses, or repeated-measures designs?

Answer 1

1. Repeated measurements on the same people on 3 or more occasions
2. The same people measured under 3 or more conditions in an experimental design
3. Three or more matched groups (e.g mother and daughter)

Question 2

Why do we use a qqplot?

Answer 2

To identify anything “unusual” such as outliers.

Question 3

What is the difference between a univariate approach and a multivariate approach?

Answer 3

Univariate:

1. Assumes sphericity
2. Assumes independent observations
3. Assumes normal distributions

Multivariate:

1. Does not assume sphericity
2. Assumes independent observations
3. Assumes normal distributions (but can be violated if not too severe)

Question 4

What is sphericity?

Answer 4

The variances of all possible difference scores between pairs of 3+ within-subject conditions being homogenous at the population level.

Question 5

When sphericity is determined, which approach is superior?

Answer 5

Univariate approach.

Question 6

What is compound symmetry?

Answer 6

A covariance matrix that has the same variance in each diagonal element and the same covariance in every off-diagonal element of the matrix.

Question 7

Can we assume that sphericity is met if there is compound symmetry?

Answer 7

Yes

Question 8

How do we calculate sphericity?

Answer 8

Using E, calculated from the observed covariance matrix. E will rang in values between 1/k and 1, when k is the number of levels.

Question 9

How do we calculate E?

Answer 9

1. Greenhouse-Geisser estimator, or

2. Huynh-Feldt estimator

Question 10

What are the steps to a within-subjects analysis?

Answer 10

1. lm() function
2. Post-processing with Anova() function (not enough alone for a within-subjects design, so we have to include additional factors e.g ordered factors for different time points)
3. Extracting the output for a multivariate approach using s() (we are interested in the term = trial output to test if the means are the same for all levels. if the p-value in the pillar results is small, the means at each time point are not equal)
4. Linear contrasts (orthogonal polynomials)
5. Extract Pillai (linear, L, Q, C, 4) which does not rely on sphericity

Question 11

What is the Pillai test used for?

Answer 11

If p is very small, then it is not consistent with the hypothesis that all mean differences are equal (so there are differences between the groups)