Module 5 Flashcards
How much do we want our DVs to be correlated?
Preferably .2-.4 would be a nice correlation. Anything above .6 is problematic
What is more important than deciding on DVs that are statistically related?
It is more important that DVs work together to explain a greater concept, rather than be correlated statistically.
What does MANOVA protect against?
MANOVA protects against inflated Type I error (only when DVs are correlated)
In what case is MANOVA more useful than just running multiple ANOVAs?
MANOVA is more useful when provides greater insight and explanation about the variables, beyond doing multiple ANOVAs
How many IVs and DVs do we require for MANOVA. What types of variables should they be?
We need at least 1 IV (continuous or categorical)
We need at least 2 continuous DVs
What is another name for the rows and columns in a matrix?
Vectors
What are two other names for the individual values in a matrix?
Components or elements
How many rows and columns are in a 3x6 matrix?
3 rows, 6 columns
What is a square matrix?
A matrix with an equal number of rows and columns
What is an identity matrix?
A matrix where the diagonal values are all 1, and the off-diagonal values are all 0
What are the 3 additional data cleaning requirements for MANOVA?
Homogeneity of matrices
Multivariate normality
Multicollinearity and singularity
What are the two assumptions underlying the assumption of homogeneity of covariance matrices?
1) The variances for each DV are equal
2) The correlation between 2 DVs is the same for all groups
It is testing the assumption that each cell of the matrix is from the same population
What statistic tells us about homogeneity of covariance matrices?
Box’s M. We want a non-significant result. This test can be ignored when sample sizes are equal because some MANOVA test statistics are robust to violations of this assumption
How does Field (2013) suggest we check for the assumption of multivariate outliers?
Check the assumption of univariate normality of residuals for each DV in turn. But this does not guarantee multivariate normality.
To avoid multicollinearity, how should we select our DVs? What correlation indicates multicollinearity?
We should select DVs that are moderately or negatively correlated. Anything above .9 or below -.9 correlation represents multicollinearity.
What are the 4 MANOVA test statistics?
1) Pillai’s trace (preferred when sample sizes are equal)
2) Wilk’s Lambda
3) Hotelling’s trace
4) Roy’s Largest Root
What does the ‘Multivariate Tests’ table tell us?
The results of the MANOVA
What does the ‘Tests of Between Subjects Effects’ tell us?
The results of the individual ANOVAs performed after the MANOVA
What is Discriminant Function Analysis?
DFA is an assessment on how a set of groups can be best discriminated using the linear variates (functions) of several predictors. i.e. how the DVs can separate the groups
How does Roy Bargman’s method work? What conditions do we require to use it?
Roy Bargman’s is a step-down method which sequentially covaries out DVs. To use it, we need to have a significant MANOVA, but non-significant individual ANOVAs. This method will show where the true differences are when ANOVAs cannot.
What is a variate? What does a significance < .05 mean for a variate?
A variate is a combination of DVs and if significant it means this variate is significantly discriminating the groups
After you’ve identified your variates, what will the ‘Standardised Canonical Discriminant Function Coefficients’ table tell you?
This table will tell us how a DV contributes to a variate. A high score means it contributes a lot, and a both positive and negative score means it contributes to the variate in opposite ways
What does the ‘Functions at Group Centroids’ table tell us?
It tells us which group are being discriminated by a variate. For a given variate, a group with positive and negative signs is being discriminated by that variate.
When testing for assumptions, when do we need to have the data split by groups?
When checking for univariate outliers/normality, and when checking linearity
Which assumption is checked in the main analysis?
Homogeneity of covariance matrices
Imagine we get a significant MANOVA, but non-significant univariate ANOVA. What does Field recommend we do? What does Hills recommend?
Field says MANOVA has more power to detect group differences, so we should trust it and follow-up with DFA.
Hills says we should follow up with Roy Bargman’s method. Remember, it’s all about how you justify using the test you choose.
In the literature, what is the most used statistic? What is the most robust?
Wilk’s Lambda is most used in literature. However, Pillai’s trace is considered most robust, especially when we have assumption violations or our sample sizes are equal
