New Exam specific MANOVA

Question 1

MANOVA is used to ask whether a combination xxx varies as a function of xxxxxx

Answer 1

MANOVA is used to ask whether a combination of (DVs) varies as a function of treatment (IVs with whatever many levels)

Question 2

What mean differences does MANOVA emphasize?

Answer 2

MANOVA emphasizes the mean differences and statistical significance of dif- ferences among groups.

Question 3

In MANOVA, a new DV that xxxx xxxx xxxxxx is created from the set of DVs.

Answer 3

maximizes group differences

Question 4

The new DV is a xxxxxxx xxxxxxxxx

Answer 4

linear composite

Question 5

combined so as to xxxx xxx xxxxx as much as possible

Answer 5

separate the groups as much as possible

Question 6

What analysis is then performed on the composite DV?

Answer 6

ANOVA

Question 7

What are the 3 main advantages of MANOVA over separate ANOVAs?

Answer 7

1) Control of type 1 error rate Alan says best reason. It reduces the need to correct for multiple comparisons. This means that the result can be tested at 0.05 significance rather than 0.025 (Bonferroni corrected) Obviously, this advantage is greater the more DVs are being used.
2) Under certain rare situations, MANOVA can show differences that would not show up with ANOVA.

When responses to two DVs are considered in combination, group differences become apparent. Thus, MANOVA, which considers DVs in combination, may occasionally be more powerful than separate ANOVAs.

This is the rare occasion when in 2 dimensions the effect becomes more prominent (ellipses)

3) By measuring several DVs instead of only one, the researcher improves the chance of discovering what it is that changes as a result of different treatments and their interactions.

Question 8

What are the 4 main DISadvantages of MANOVA over separate ANOVAs?

Answer 8

1)

Usually lack of power (usually) Cole paper

Same group is higher on both/all DVs.

DVs that are positively correlated or same direction at least (make that overlapping cigar shape in 2D space, whereby they point in the same direction).

IF IT WERE IN THE OPPOSITE DIRECTION (NEGATIVE CORRELATION) IT WOULD BE EXTREMELY HIGH POWER

2)

requires homogeneity of variance as with ANOVA but also requires homogeneity of Variance-Covariance matrix

3)

more complex to interpret (ambiguous as to where effect lies) - we dont really know which DV is responsible etc

4)

not designed to look at differential effects on separate DVs (so bad if that is your goal) - PSYCH’S ALWAYS WANNA OPEN UP

Question 9

Details about homogeneity of variance for MANOVA

What does MANOVA require?
What is test?
What is output desired from test?

Answer 9

Requires Homogeneity of variance / COVARIANCE matrices- all variance for all DVs! ALL have to be equal across the groups of the IVs.

use Box’s test of equality of variance –covariance

if significant = violation

Question 10

4 ways to test MANOVA statistically?

Answer 10

Roy’s largest root
Hotelling’s trace,
Wilks lambda,
Pillai’s trace

all basically the same - slight variations that i can’t be bothered to remember - all need to be significant and all are converted to F statistic

Question 11

Outline the 3 main similarities between (ANOVA) with between-groups factors, and its multivariate equivalent (“classical” MANOVA).

Answer 11

Both will give you two main effects and an interaction

Plus the abilities to look at contrasts (trends, simple main effects etc).

Both report tests as F-ratios (even if these are approximate in some MANOVAs)

Question 12

Outline the 3 main differences between (ANOVA) with between-groups factors, and its multivariate equivalent (“classical” MANOVA).

Answer 12

1) The DV – in ANOVA there is a single DV (univariate) whereas there are multiple DVs (multivariate) in the MANOVA. These are combined together in a linear weighted fashion to form a single composite DV for each of the effects tested in the MANOVA.
2) This also results in some differences in assumptions: eg whereas ANOVA requires homogeneity of variances in the DV across groups; the MANOVA requires homogeneity of variance-covariance matrices across groups
3) test statistics: there are 4 for MANOVA (Wilks lamda etc) whereas only 1 (F-ratio) for ANOVA

Question 13

Outline the 2 main (obvious) similarities between classical MANOVA and repeated measures MANOVA

Answer 13

the main similarities are that both have multiple DVs and produce F-test assessment of effects

Question 14

Highlight the 4 key differences between classical MANOVA and repeated measures MANOVA

Answer 14

1)

DVs - Measurement

Typically in the way the multiple DVs are measured: different variables measuring the same construct measured at the same time in the case of MANOVA, repeated measures on the same variable, typically at different times, in repeated measures MANOVA. (It is possible to apply RM analyses to different measures taken at the same time

2)

DVs Segments vs Composites

The way the multiple DVs are combined: in classical MANOVA the composite DV is a weighted linear combination of the DVs which maximally differentiates the groups in the effect concerned. In repeated-measures MANOVA the DVs are formed by pairwise differences between the DVs (DV1- DV2; DV2 - DV3 etc) - SEGMENTS

3)

Different kind of effect comparison questions

Imagine a design with 2 groups with 3 DVs.

In the case of the classical MANOVA there would just be an effect of the group factor.

In the RM MANOVA, there is an effect of group, an effect of measure (over the 3 DVs) and an interaction effect of group*measure.

Thus techniques asks different questions.

4) . Also, the variable have to be on the same scale for meaningful RM MANOVA whereas this is not required for classical MANOVA

Question 15

What happens if you add more DVs to MANOVA?

Answer 15

The power of the MV tests generally declines as the number of DVs is increased.

The cigar problem gets worse in multi-dimensional space

Question 16

what does a multivariate MONOVA hypothesis ask?

Answer 16

Does treatment have an effect on the ‘intellectual ability’ (combination of reading/arithmetic etc) make up label for composite.

Main effects of IVs
H0: IV has no systematic effect on the optimal linear combination of DVs (LC)

Interactions among IVs
H0: Change in the LC over levels of one IV does not depend on the level of another IV

Question 17

what does a univariate hypothesis ask?

Answer 17

Does treatment have an effect on reading performance? Does treatment have an effect on arithmetic?

Question 18

it’s basically better to do separate

Answer 18

anovas

Question 19

what Specific Comparisons would you wanna make in MANOVA?

Answer 19

e.g. Which levels of IV main effect (which groups) are different from which others?

Question 20

What are the 3 main assumptions of MANOVA?

Answer 20

1) Independent observations
2) Observations on the DVs follow a multivariate normal distribution in each group
3) Population covariance matrices of DVs for the groups are equal (homogeneity of variance- covariance matrices)

Question 21

what is the danger of the Independent observations assumption?

Answer 21

If you were to accidentally include the same subject several times, or you entered the same data values into a computer more than once, or, if our subjects tell future subjects something about the experiment, then we have a form of non-independence. Each subject’s data may not be independent of other subject’s data.

“Whenever the treatment is individually administered, observations are independent; but where treatments involve interaction among individuals, such as discussion method of group counseling, the observations may influence each other.” Glass & Hopkins (1984)

While independence is a requirement of the statistical techniques, the means of dealing with it are not; instead, the independence requirement places constraints on the conduct of the experiment itself. The remedy for independence problems is a procedural matter and is really a part of an experiment’s internal validity.

Question 22

which is more strict - univariate or multivariate normailty assumption and why?

Answer 22

Multivariate normality is a much stricter condition than univariate normality
– All of the individual DVs have normal distribution
– Any linear combination of DVs have normal distribution
– All subsets of the set of variables have a multivariate normal dist.

Question 23

the homogeneity of variance assumption is usually ok if….

Answer 23

equal group sizes

Question 24

Back to the power of DVs in MANOVA. What two main things will reduce power?

Answer 24

1)

If the DVs are too POSITIVELY correlated (i.e. they will overlap in dimensional space - so their effect sizes will be reduced as overlapping)

2)

If too many DVs in te first place, they will probably correlate more as they attempt to measure the same thing. This will reduce power. More DVs = less power

Question 25

What should more DVs be able to tell us?

Answer 25

About the convergent and divergent validity of our measures

Question 26

And what is the irony of achieving convergent or divergent validity in MANOVA?

Answer 26

A reduction of power due to multiple DVs and positively correlated relationships

Question 27

what is a main effect in MANOVA asking?

Answer 27

Holding all else constant, are mean differences in the composite DV among groups at different levels of an IV larger than expected by chance?

Question 28

what is a interaction effect in MANOVA asking?

Answer 28

Holding all else constant, does change in the DV over levels of one IV depend on the level of another IV?

Question 29

With more than two IVs, there are multiple interactions. How are they tested?

Answer 29

With more than two IVs, there are multiple interactions. Each interaction is tested separately from tests of other main effects and interactions, and these tests (but for a common error term) are independent when sample sizes in all cells are equal.

Question 30

SO the best choice is a set of DVs that are ….

Answer 30

are uncorrelated with each other because they each measure a separate aspect of the influence of the IVs.

Question 31

Practical Issues

Answer 31

Practical Issues

Question 32

what happens if any missing data?

Answer 32

as experiments are complicated by numerous DVs and, perhaps, covariates, the probability of missing data increases - and is a real problem

Question 33

In addition, when using MANOVA, it is necessary to have more xxxxx than xxxxx in every cell.

Answer 33

In addition, when using MANOVA, it is necessary to have more cases than DVs in every cell. With numerous DVs, this requirement can become burdensome, especially when the design is com- plicated and there are numerous cells.

Question 34

There are two reasons for the requirement. what is the first ?

Answer 34

The first is associated with the assumption of homogeneity of variance–covariance matrices (see Section 7.3.2.4). If a cell has more DVs than cases, the cell becomes singular and the assumption is untestable. If the cell has only one or two more cases than DVs, the assumption is likely to be rejected. Thus, MANOVA as an analytic strategy may be discarded because of a failed assumption when the assumption failed because the cases-to-DVs ratio is too low.

Question 35

second?

Answer 35

Second, the power of the analysis is lowered unless there are more cases than DVs in every cell because of reduced degrees of freedom for error.

Question 36

Power in MANOVA also depends on the relationships among DVs. Power for the multivariate test is highest when ….

Answer 36

the pooled within-cell correlation between two DVs is high and negative.

Question 37

as standard assumptions, MANOVA requires

Answer 37

multivariate normality
Absence of Outliers
Homogeneity of Variance–Covariance Matrices
Linearity
Absence of Multicollinearity and Singularity

Question 38

what is Homogeneity of Variance–Covariance Matrices?

Answer 38

The assumption is that variance– covariance matrices within each cell of the design are sampled from the same population variance– covariance matrix and can reasonably be pooled to create a single estimate of error.

Question 39

If sample sizes are xxxx and Box’s M test is significant at p=?, then robustness is not guaranteed.

Answer 39

However, if sample sizes are unequal and Box’s M test is significant at p