Week 8-MANOVA Flashcards
What is MANOVA?
■ Stats tests you’ve learnt so far have looked only at the effect of IVs on one dependent variable.
■ Multivariate ANalysis Of Variance
■ We use this when we have one IV and many dependent variables
■ E.g. The effect of pet ownership on mental health (1 IV)
■ Mental health = Depression, Anxiety, Schizoid disorders, Substance dependence, Phobias etc (i.e. Many DVs!)
■ More DV’s = increased chance of a Type 1, (false positive) errors.
Why not run multiple ANOVAs?
■ Why not run 5 ANOVA’s?
Type 1 Error rate (falsely rejecting H0)
- alpha (or α = .05) is for 1 test.
■ Our example would produce 5 p values separately
■ .955 = .774
■ 1-.774
■ Our critical level of statistical significance is now .226 (1 in 5 chance of finding a statistical significant effect)
■ False positive increases!
What does the MANOVA assess?
■ The MANOVA assesses whether your IV has an overall effect on your variables taken together e.g. Does pet ownership effect mental health
■ This is assessed using a single p value
■ If it is significant, you can then look at the second part of the MANOVA, which specific aspects of mental health does it significantly effect
■ This is often called the multivariate test; it is sometimes referred to as an omnibus test although this is somewhat ambiguous
What are multivariate tests?
-Pillai’s Trace (report this!)
-Robust to minor violations
What is the reason for doing MANOVAs?
■ To avoid false positive results through repeated testing
■ If you have a significant Multivariate test then you can look at the effect of the IV on the DVs separately
What are the assumptions of a MANOVA?
■ Usual ANOVA assumptions
■ In a multivariate ANOVA the IV will always be between-subjects
■ Levene’s (homogeneity of variance) will be calculated for each DV (you want them to be non-sig)
■ Box’s test will also be produced, this tests equality in covariance matrices (only a concern if p<.001 as ot will not meet the assumption)
MANOVA will produce which 2 homogeneity tests?
- Box’s Test- equality of covariance matrices (one test related to all DV’s)
– Simply put you want this to be p>.001, if not sig it means the p-value taken from the multivariate test box in the output is reliable - Levene’s test for equality of error variances (sep test for each DV, in this example 4).
– Simply put you want this to be non sig p>.05, if not sig it means each p value for each DV taken from the between-subjects contrasts box is reliable
What will the MANOVA output give you?
■The output will give a multivariate test which assesses whether your IV has an effect on your DV’s (overall).
■This will give you an F value, degrees of freedom and a p value just like any ANOVA
but also gives four other measures
■ Pillai’s Trace
■ Wilks’ Lambda
■ Hotelling’s Trace
■ Roy’s Largest Root
■ With two levels to the IV it doesn’t matter which of these is used (F-statistic will be
identical).
■ A two level IV doesn’t need post hoc testing but this example had a three level IV!
What are the MANOVA Stopping Rules?
-If the multivariate test is not sig then STOP!
-If an individual ANOVA is not sig then STOP! only report those that are sig
-If it does not have more than 2 levels then STOP! (because we know where the difference is with 2)
If all these are sig and more than 3 levels, then you will do post hoc!
What is Homogeneity of variance?
– The variances found in each condition relatively even, if not then the individual ANOVAs (not the multivariate test) are not valid
– Tested with Levene’s test, and a separate Levene’s test is given for each DV
– If this assumption is violated, we could run a Welch tests instead
What is the Equality of Covariance Matrices?
■Whether the correlations between any two measured DVs is similar to the other correlations between all other DVs
■Box’s test is computed for this.
■You want Box’s test to be non-significant (like other ANOVA assumption tests)
■However, unlike the others it is only an issue if p<.001
