### Multivariate Statistics

```Multivariate Statistics
An Introduction &
Multidimensional Contingency Tables
What Are Multivariate Stats?
• Univariate = one variable (mean)
• Bivariate = two variables (Pearson r)
• Multivariate = three or more variables
simultaneously analyzed
One-Way ANOVA
• Could consider bivariate – one grouping
variable, one continuous variable.
• Could consider multivariate – predict Y
from the set of k-1 dichotomous dummy
variables coding the grouping variable.
Factorial ANOVA
• I consider it multivariate – one continuous
variable and two or more grouping
variables.
• Some call it univariate, as in “univariate
ANOVA.” Here the focus is on how many
comparison variables there are (only one
Y).
• If there were more than one Y, they would
call it MANOVA and consider it
multivariate.
Independent and Dependent
Variables
• Data analyzed with multivariate techniques are
most often nonexperimental.
• You know how I feel about using the terms
“independent variable” and “dependent variable”
in that case.
• But others use these terms more loosely.
• Independent = grouping, prior, known, thought to
be the cause.
• Dependent = continuous, later, predicted,
thought to be the effect.
Descriptive vs. Inferential
• Like univariate and bivariate stats,
multivariate stats can be used
descriptively.
• In this case, there are no assumptions.
• If you use 2, t, or F, then there are
assumptions.
Rank Data/Scale of Measurement
• Only God knows if your data are interval
rather than merely ordinal, and she is not
saying.
• Ordinal data may be normally distributed.
• Interval data may not be normally
distributed.
• Ranks are not normally distributed, but
may be close enough to normal.
Why Use Multivariate Stats?
•
•
•
•
To obfuscate.
Because SPSS makes it so easy to do.
To statistically hold constant the effects of
confounding variables in nonexperimental
research.
Why NOT use Multivariate Stats?
your research question with more simple
analysis.
• One may be able to get pretty much any
damn results she wishes, so why bother?
• Do you really understand what is going on
out there in hyperspace? I am already
confused enough in three dimensional
space.
Multidimensional Contingency
Table Analysis
• Chapter 17 in Howell.
• Have three or more dimensions in the
contingency table. All variables are
categorical.
• Moore, Wuensch, Hedges, & Castellow
(1994)
• Simulated civil case, sexual harassment.
• Female plaintiff, male defendant.
The Design
• Physical attractiveness (PA) of defendant,
manipulated.
• Social desirability (SD) of defendant,
manipulated.
• Sex/gender of mock juror.
• Verdict recommended by juror
(dependent).
• Experiment 2: manipulated PA and SD of
litigant.
Logit Analysis
• This is a special case.
• One variable is identified as dependent.
• We are interested only in effects that
involve the dependent variable.
Earlier Research
• Physically attractive litigants are better
treated by the jurors. No Social
Desirability manipulation.
• But jurors rated the physically attractive
litigants as more socially desirable
(intelligent, sincere, and so on).
• Which is directly affecting the verdict, PA
or inferred SD ?
More Earlier Research
• Follow-up to that just described.
• Manipulated only the SD of the litigants.
• Socially desirable litigants were treated
better by the jurors.
• But the jurors rated the (never seen)
socially desirable litigants as more
physically attractive.
• Still do not know if it is PA or SD that
directly affects the verdict.
Experiment 1(manipulate
characteristics of defendant)
• Guilty verdicts were more likely when
– Juror was female
– Defendant was socially undesirable
• Gender x PA Interaction: Female jurors:
– Judged the physically attractive defendants
more harshly
– Maybe they thought the defendants used their
PA to take advantage of the plaintiff.
• No significant effect of PA among male
jurors.
Experiment 1(manipulate
characteristics of plaintiff)
• Judgments in favor of plaintiff more
frequent when she was socially desirable.
• No other effects were significant.
• Strength of effect estimates in both
experiments showed effect of SD much
greater than effect of PA.
Conclusions
• When jurors have no relevant info on SD,
they infer that the beautiful are good, and
that affects their verdicts.
• When jurors do have relevant info on SD,
the PA of the litigants is of little
importance.
```