MANOVA Flashcards

1
Q

What is MANOVA and what are its features

A

MANOVA is a multivariate technique that looks at group differences across multiple DVs
It is useful for when a DV is can’t be captured by a single variable
considers combined effects of the DVs and how they work together to separate groups

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2
Q

Why are multiple ANOVAs not appropriate

A

understanding of resulting MANOVA effects may not be gained by studying the significance of multiple ANOVAs
A significant MANOVA difference need not imply that any significant ANOVA effect/s exist

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3
Q

Situations when multiple ANOVAs are appropriate

A
  1. when the DVs are conceptually independent
  2. when research being conducted is exploratory in nature
  3. when outcome variables have previously been studied in a univariate context
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4
Q

what is the variable selection problem

A

if fewer outcome variables than total number initially chosen should form a basis for interpretation

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5
Q

what is the variable ordering problem

A

to make an assessment of the relative contribution of the outcome variables to the resultant group differences or to the resultant effects of the treatment variable

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6
Q

when is MANOVA most appropriate

A

when DVs are highly negatively correlated and when they are moderately correlated in either direction

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7
Q

what are the advantages of MANOVA

A
  1. controls Type 1 error rate compared to a series of multiple ANOVAs
  2. looks at combined effects of all DVs
  3. if there are low number of DVs, can be more powerful than a series of ANOVAs
  4. inclusion of more DVs can result in a more robust model where sig effects are more likely to be found with reduced error variance
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8
Q

what are the disadvantages of MANOVA

A
  1. complex multivariate technique - issues with interpretation
  2. questionability about whether it can actually control Type 1 error rate
  3. selection of DVs require strong theoretical justification
  4. redundancy with inclusion of highly correlated DVs
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9
Q

What does Wilk’s Lambda measure

A
  • The amount of variance in the variate not accounted for by the IV
  • If multiple DVs, then the final value will be the product of the unexplained variance from each variate
  • most commonly used and appropriate when assumptions are met
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10
Q

what does Pillai’s Trace measure

A
  • The amount of variance in the variate accounted for by the IV
  • If multiple DVs, the final value is the sum of explained variance in the variate
  • robust to assumption violations and when sample sizes are equal
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11
Q

Roy’s Largest Root vs Hotellings T squared

A
  • Both look at eigenvalues
  • Hotellings looks at explained variance/unexplained variance for EACH variate
  • Roy’s only looks at it for first variate (very powerful if only one variate in analysis and assumptions are met)
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12
Q

What does the ‘on-diagonal’ measure in a matrix

A

sum of squared deviations of scores from the mean for that variable

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13
Q

What does the ‘off-diagonal’ measure in a matrix

A

represents the combined effects of the DVs

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14
Q

How is the final MANOVA statistic determined

A

Hypothesis SSCP matrix/error SSCP matrix

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15
Q

What are MANOVA specific assumptions

A
  1. Homogeneity of covariance matrices
  2. Multivariate Normality
  3. Multicollinearity and singularity
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16
Q

What does the homogeneity of covariance matrices look at

A
  • assumes that variance for each DV must be roughly equal AND the correlation between any two dependent DVs are similar in all groups
17
Q

when can you justifiably omit testing multivariate normality

A

when cell size is greater than 30 - MANOVA is considered robust to violations of normality

18
Q

What does multicollinearity expect

A

that the DVs should be moderately or negatively correlated with each other