design involving 3 or more dependent groups examples
- same people, 3 diff time points
- same people, 3 different conditions
- 3 matched groups (triplets)
what is univariate approach
- within-subject design
- assumes sphericity
what is multivariate approach
- does not have assumption of sphericity
- not superior to univariate approach
is multivariate approach better than univariate?
no and depends. if data does not violate sphericity then univariate is better. but multivariate will be better if there is violence in sphericity
what is sphericity?
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.
what is compound symmetry
it is the covariance just means that all the variances are equal and all the covariances are equal.
is compound symmetry determined by values?
no. pattern. as long as there are only 2 values: diagonal and off diagonal values.
if compound symmetry is not there. can we still assume no violation of sphericity?
yes. compound symmetry is sufficient but not NECESSARY for sphericity
should we assume sphericity?
if design is based on matched groups (triplets) then can assume. but if based on repeated sample then dont
how is sphericity calculated?
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
how is sphericity calculated?
- 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
if we have 9 levels in out design, what is the range of our sphericity?
1/9 to 1 (perfect sphericity)
2 ways to estimate e in sample data
- greenhouse (e hat)
- huynh (e with curly dash on top)
in extracting multivariate results, what output do we pay attention to?
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)
what is the main part of interest in multivariate contrast analysis for polynomial effects?
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
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)
means that over the 5 time periods, there is average REDUCTION (change) of OBSERVED migraine occurrence of 12
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)
means that over the 5 time periods, there is average REDUCTION (change) of migraine occurrence of 3 standard deviation units
