PG MANOVA Flashcards
What is MANOVA
Ð ANOVA with multiple DVs
Ð Mean diffs between groups or combinations of DVs
Ð Math same as discriminant function analysis, so we are mathematically constructing a DV which maximises the diff between the factors, and does it each separately for each factor. New DVs are linear combination of DVs.
Ð Different combination of DVs for each effect in design.
why manova?
MANOVA is especially appropriate when the investigator has gathered a system of dependent variables to address a multivariate hypothesis. A variable system is “loosely defined as a col- lection of conceptually interrelated variables that, at least potentially, determines one or more meaningful underlying variates or constructs”
Why measure same DV several different ways, or analyse or measure multiple DVs?
Ð Capturing broader and richer information
Ð Any IV that is valuable is likely to affect participants in more than one way…. Say, psychological and physiological distress (e.g. stress intervention might affect physiological (heart rate / ski conductance) & emotional (scale report) & observational etc etc. Some people say bung in a load of measures so you catch any effect possible. But this is slightly dubious. \
when you run a MANOVA with 4 DVs …. what else do you get in the output?
4 separate ANOVAs - useful to save time
if you must run post-hoc tests, which one?
tukey
one assumption is critical here…. that is?
homogeneity of varaince-CO-VARAINCE matrices
how does one test for CO-VARAINCE?
in multivariate = Box’s test =
What is the ANOVA version to test for homogeneity of variance?
Levene’s test
what does Levene’s test care about
variance BETWEEN GROUPS
what are the 4 tests for MANOVA?
Ð Pillai’s trace (Bartlett) – most robust against violations of assumptions (when N equal) + best when var is >1 variate
Ð Wilk’s Lambda
Ð Hottelling’s Trace
Ð Roy’s Largest Root - powerful if diff is on first variate
what are the advantages of MANOVA over ANOVA?
Ð Multiple DVs increase chance of getting an effect
Ð Protection against type-1 error inflation (finding effect when there is none by chance as running so many separate ones – think frmri)
Ð Can (rarely show effects not possible in ANOVA) - Ð Sometimes might have more power
Ð More separation in 2D than you could get in 1D between the 2 alone. Happens super rare. (THIS IS WHERE COLE PAPER COMES IN)
what are the disadvantages of MANOVA over ANOVA?
Ð ADDITIONAL assumption
Ð Vague and ambiguous outcomes (omnibus)
Ð Usually LOWER POWER (see cole)
Ð POWER declines when adding more DVs
Ð On the very reason you might want MANOVA (multiple DVs) – actually you reduce power anyway.
what was alans take home message?
TAKE HOME MESSAGE: THE WAY VARIABLES WORK, IT’S GEN CASE THAT MANOVA WILL COME OUT WITH A LOW POWER COMBINATION
MANOVA vs RM MANOVA
MANOVA vs RM MANOVA
Ð RM MANOVA = profile analysis = each repeated measure is a DV (only when >3 levels)
Ð MANOVA calculations use the scores from the k DVs
Ð RM MANOVA calculations use (k-1) transformed DV scores (e.g. the k-1 differences (segments) between adjacent scores).
MORE POWER using a univariate measure (see RM MANOVA)
what is Doubly multivariate?
Doubly multivariate = MANOVA with RM (when RM is a composite DV like in this lecture)