Lecture 8

Question 1

design involving 3 or more dependent groups examples

Answer 1

• same people, 3 diff time points
• same people, 3 different conditions
• 3 matched groups (triplets)

Question 2

what is univariate approach

Answer 2

• within-subject design

- assumes sphericity

Question 3

what is multivariate approach

Answer 3

• does not have assumption of sphericity

- not superior to univariate approach

Question 4

is multivariate approach better than univariate?

Answer 4

no and depends. if data does not violate sphericity then univariate is better. but multivariate will be better if there is violence in sphericity

Question 5

what is sphericity?

Answer 5

important assumption of a repeated-measures ANOVA.

it s the condition where the variances of the differences between all combinations of related groups (levels) are equal.

Question 6

what is compound symmetry

Answer 6

it is the covariance just means that all the variances are equal and all the covariances are equal.

Question 7

is compound symmetry determined by values?

Answer 7

no. pattern. as long as there are only 2 values: diagonal and off diagonal values.

Question 8

if compound symmetry is not there. can we still assume no violation of sphericity?

Answer 8

yes. compound symmetry is sufficient but not NECESSARY for sphericity

Question 9

should we assume sphericity?

Answer 9

if design is based on matched groups (triplets) then can assume. but if based on repeated sample then dont

Question 10

how is sphericity calculated?

Answer 10

from the observed covariance matrix by e
e is the parameter when calculated on a population covariance matrix and it is a sample statistic when estimated on a sample covariance matrix

Question 11

how is sphericity calculated?

Answer 11

• from the observed covariance matrix by e (the coefficient of sphericity)
• e is the parameter when calculated on a population covariance matrix and it is a sample statistic when estimated on a sample covariance matrix
• if there are k levels in the design, the range for sphericity is 1/k - 1. where 1 is perfect sphericity

Question 12

if we have 9 levels in out design, what is the range of our sphericity?

Answer 12

1/9 to 1 (perfect sphericity)

Question 13

2 ways to estimate e in sample data

Answer 13

• greenhouse (e hat)

- huynh (e with curly dash on top)

Question 14

in extracting multivariate results, what output do we pay attention to?

Answer 14

the pillai criterion under multivariate tests: trial

if p value is lower than alpha, means reject h0. which means that from the null hypothesis test, the within-subject means for all levels are NOT the same (there is a difference)

Question 15

what is the main part of interest in multivariate contrast analysis for polynomial effects?

Answer 15

the multivariate pillai result for each linear, quadratic, cubic, quartic rates of change over time.

• linear result indicates change over the … time points (either increase or decrease linearly)
• the others are indicative of non-linear effects of change in dv which is also found over the time course

Question 16

in linear effect, how could we interpret the value of observed contrast mean of -12

• dv: no of migrain
• IV: 5 time course (baseline 1, bs 2, week 3, 4, 5)

Answer 16

means that over the 5 time periods, there is average REDUCTION (change) of OBSERVED migraine occurrence of 12

Question 17

in linear effect, how could we interpret the value of STANDARDISED contrast mean of -3

• dv: no of migraine
• IV: 5 time course (baseline 1, bs 2, week 3, 4, 5)

Answer 17

means that over the 5 time periods, there is average REDUCTION (change) of migraine occurrence of 3 standard deviation units