New Exam specific MANOVA Flashcards
(39 cards)
MANOVA is used to ask whether a combination xxx varies as a function of xxxxxx
MANOVA is used to ask whether a combination of (DVs) varies as a function of treatment (IVs with whatever many levels)
What mean differences does MANOVA emphasize?
MANOVA emphasizes the mean differences and statistical significance of dif- ferences among groups.
In MANOVA, a new DV that xxxx xxxx xxxxxx is created from the set of DVs.
maximizes group differences
The new DV is a xxxxxxx xxxxxxxxx
linear composite
combined so as to xxxx xxx xxxxx as much as possible
separate the groups as much as possible
What analysis is then performed on the composite DV?
ANOVA
What are the 3 main advantages of MANOVA over separate ANOVAs?
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.
What are the 4 main DISadvantages of MANOVA over separate ANOVAs?
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
Details about homogeneity of variance for MANOVA
What does MANOVA require?
What is test?
What is output desired from test?
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
4 ways to test MANOVA statistically?
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
Outline the 3 main similarities between (ANOVA) with between-groups factors, and its multivariate equivalent (“classical” MANOVA).
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)
Outline the 3 main differences between (ANOVA) with between-groups factors, and its multivariate equivalent (“classical” MANOVA).
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
Outline the 2 main (obvious) similarities between classical MANOVA and repeated measures MANOVA
the main similarities are that both have multiple DVs and produce F-test assessment of effects
Highlight the 4 key differences between classical MANOVA and repeated measures MANOVA
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
What happens if you add more DVs to MANOVA?
The power of the MV tests generally declines as the number of DVs is increased.
The cigar problem gets worse in multi-dimensional space
what does a multivariate MONOVA hypothesis ask?
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
what does a univariate hypothesis ask?
Does treatment have an effect on reading performance? Does treatment have an effect on arithmetic?
it’s basically better to do separate
anovas
what Specific Comparisons would you wanna make in MANOVA?
e.g. Which levels of IV main effect (which groups) are different from which others?
What are the 3 main assumptions of MANOVA?
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)
what is the danger of the Independent observations assumption?
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.
which is more strict - univariate or multivariate normailty assumption and why?
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.
the homogeneity of variance assumption is usually ok if….
equal group sizes
Back to the power of DVs in MANOVA. What two main things will reduce power?
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
