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)
what are the 3 main assumptions of MANOVA?
1) INDEPENDENT OBSERVATIONS
2) OBSERVATIONS ON THE DV FOLLOW A MULTIVARIATE NORMAL DISTRIBUTION IN EACH GROUP
3) POPULATION COVARIANCE MATRICES OF DVs FOR THE GROUPS ARE EQUAL (HOMOGENIETY OF VARIANCE-COVARIANCE MATRICES)
details of INDEPENDENT OBSERVATIONS ?
Ð SERIOUS IS VIOLATED
Ð Dependant obs occur quite often in social science (e.g. co-operative learning / assessments of teaching methods)
Ð METHODS for dealing with: more stringent alpha / use multivariate analysis technique
details of MULTIVARIATE NORMAL DISTRIBUTION?
Ð In UNI-variate - Only slight effect on power and effect as of central limit theorem and sampling distribution
Ð In MANOVA MULTI-variate: much stricter.
Ð All individual DVs need normality + any linear combination + any subsets of variables have multivariate normality – check scatterplots of each pair (cigar shaped – elliptical)
Ð IF VIOLATED
Ð Makes test unreliable as with ANOVA
Ð More serious with small sample sizes
details of HOMOGENIETY OF VARIANCE-COVARIANCE MATRICES?
Ð MANOVA different from RM MANOVA
Ð MANOVA between groups = (HOMOGENIETY OF VARIANCE-COVARIANCE MATRICES)
Ð RM MANOVA = Sphericity (homogeneity of covariance)
Ð Keep the group sizes equal as always
ALWAYS make correction when doing subsequent individual ANOVAs after – just use Bonferroni as easy to remember, but more conservative.
what are the basics of step-down analysis ?
Ð Tests each DV in riority order
Ð Establishes if each DV is affected by group treatment after controlling for effect of other higher priority DVs
Ð Highest priority DV is tested by ANOVA, and the rest are using ANCOVA
Ð Each successive DV is tested with higher priority DVs as covariates
Issue with multiple comparisons and differential weighting of alpha correction (a priori, imp variables are given more stringent corrections and vice versa)
how does one calculate bonferroni ?
alpha divided by the number of tests
Box’s test - what does it need to be?
Tabachnick and Fidell say that Box’s test is sensitive: as a rule of thumb you only really need worry if unequal sample sizes and p < .001. If you were worried, or if it was worse, you could review data screening, e.g. were we too liberal with outliers, should we consider a transformation? See T&F for further discussion.
if we check Box’s, we should also check…..?
Since the question asks about homogeneity tests in the plural, we might note at this point that Levene’s test (for the univariate tests)
What other detail in the output can we use with a rule of thumb to garner equal variance past Box’s and Levene’s?
Note the ratios of the relevant SDs (must not be greater than 4:1. As a rule of thumb this means that we can proceed with the Anova)
how to check Mahalanobis distance/?
run regression with variables
click save MD
The MD measure is compared against the critical value of the chi-squared distribution with p=0.001 and df=8 (the number of variables involved).
