KHA350 Lecture Notes - Lecture 10: Sphericity, Repeated Measures Design, Discriminant Function Analysis
25 Jun 2018
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Research methods week 10: MANOVA
MANOVA: Multiple dependent variables
- the type of experimental design for which a multivariate ANOVA may be
appropriate
- some of the limitations and assumptions
- both do the same as uni-variate; but about multiple DVs
- already done the MV version of repeated measures design
Multivariate ANOVA:
- Examine the ways in which multiple IV(s) affect DVs
oIf there are several aspects to the concept you’re measuring
oIf the DV can be operationalized in a number of ways that aren’t
necessarily highly correlated
oIf you’re interested in how the groups differ across a combination of
the DVs
Discriminant function analysis
How you can differentiate your groups with different
combinations
- When there is more than one DV, multivariate analysis of variance may be
used to perform tests on the means of a linear combination of the DV
oMANOVA technique
oTests for differences between the levels of you DV on a linear
combination
oTo combine variable together
oLooking at differences across the variables
- How this is different to repeated measures design:
oHard to tel; measuring multiple DVs, are they within subjects, or not
oRepeated measures:
Where the same people receive different treatments but the
same DV was measured for each treatment
Where the same people receive a number of different tests
Where the tests are all on the same scale
This specific situation is also referred to as profile
analysis
Where the same variable is measured at several points in time
oMANOVA allows analysis of several DVs that may be on different
scales
Giveaway: is that MANOVA has multiple measurements on
different scales
When do we use MANOVA and what is the benefit:
- goal of the design: is to discover whether behaviour, as reflected by the DVs,
is changed by manipulation of the IVs
olower type one error rate than calculating several univariate ANOVAs
for each DV
oMEASURING in multiple different ways; the combination of the the
measurements makes it easier to tell the difference between the IVs
- Data requirements:
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oGood theoretical reason for looking at multiple DVs: the combined
DVs
If they don’t conceptually related to one another, this is bad
oShould be moderately correlated
Not too highly or poorly correlated
Cant combine them artificially
If uncorrelated use separate ANOVAs with bonferroni adjusted
p values
If too highly correlated there is a redundancy of information
which loses power
May be due to:
Multicollinearity: very high correlations between
variables
Singularity: one variable is a combination of a number
of others in the analysis
oOne of the DVs come from combination of the
other variables in the set
oEg. WAIS subscores
0.25 cut off
othe number of DVs should be less than the number of cases
- Assumptions:
oIndependence of observations
oMultivariate normal distribution
Sampling distribution of the means of the DVs and all linear
combinations need to be normally distributed
Particular sensitive to outliers
Should be robust if same size is substantial
Error term > 20 or >20 participants in smallest group if
unequal sample sizes
Test by checking univariate normality and by checking for
outliers (+ or – 2 SD)
oHomogeneity of variance: across cells
For each group and correlation between DVs needs to be the
same in each group
Assumes that the data in each cell comes from a single
population and so variances can be pooled to make a single
estimate error
Test by checking
Levenes
Box’s test: homogeneity of variance-covariance
matrices
oIf significant: driven by outliers
oWhat to do if significant, look at Levenes (for
each of the DVs)
If one of those is significant then it gives
you an idea of where to look in your data
set
Have a hunt for typos or outliers
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find more resources at oneclass.com
- Different tests of significance of the combined effect:
oF value based on the basis of what the multivariate statistic is
oWilks Lambda (^): Recommended
Trust unless data set is looking untrustworthy
Small sample sizes
Unequal numbers in each group
Unexplained variance, so variance accounted for by the
best linear combination of DVs
oPillai’s trace (v): Recommended
More appropriate if there are concerns in the data set
Less powerful overall if all assumptions are met; more
powerful when not all assumptions are met
Value if the proportion of explained variance
Measure of effect size
Proportion of variance accounted for by the best linear
combination of DVs
- What if MANOVA is significant:
oSeparate univariate tests of all DVs
If correlations between DVs are low
Why do we bother putting DVs together if we are going to take
them apart anyway??
ERROR RATE: every time you do an analysis 5% chance; by
doing them in one analysis you have protected yourself against
making a type one error rate
When separated: may need Bonferroni
oStep down analysis:
Deal with this next week
oDiscriminant function analysis: honors and beyond
- What if the MANOVA is not significant:
oDon’t have justification for running separate univariate analysis
anyway
o5% chance of making errors; if one comes out as significant but
another doesn’t, hard to say that this significance isn’t due to type one
error
ojustify and make clear to audience that this is very unlikely to be type
one error
report the effect size
may cautiously suggest a trend
- Worked example:
oOne row for each participant
oOne column for IV and a column for each of the DVs
oSame as ANOVA except multiple DVs
oMultivariate analysis in SPSS:
More room for DVs
Can include covariate
Descriptive, power, effect size, plots
oBox’s test:
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
How you can differentiate your groups with different combinations. How this is different to repeated measures design: hard to tel; measuring multiple dvs, are they within subjects, or not, repeated measures: Where the same people receive different treatments but the same dv was measured for each treatment. Where the same people receive a number of different tests. Where the tests are all on the same scale. This specific situation is also referred to as profile analysis. Where the same variable is measured at several points in time: manova allows analysis of several dvs that may be on different scales. Giveaway: is that manova has multiple measurements on. Data requirements: good theoretical reason for looking at multiple dvs: the combined. If they don"t conceptually related to one another, this is bad: should be moderately correlated. If uncorrelated use separate anovas with bonferroni adjusted p values. If too highly correlated there is a redundancy of information which loses power.
