An Introduction amp Multidimensional Contingency Tables What Are Multivariate Stats Univariate one variable mean Bivariate two variables Pearson r Multivariate three or more variables simultaneously analyzed ID: 141113
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Slide1
Multivariate Statistics
An Introduction &
Multidimensional Contingency TablesSlide2
What Are Multivariate Stats?
Univariate = one variable (mean)
Bivariate = two variables (Pearson
r
)
Multivariate = three or more variables simultaneously analyzed Slide3
One-Way ANOVACould 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.Slide4
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.Slide5
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
.
HS-GPA predicted from GRE and College-GPA ??Slide6
Descriptive vs. InferentialLike 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.Slide7
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.Slide8
Why Use Multivariate Stats?To impress your friends.
To obfuscate.
Because SPSS makes it so easy to do.
To statistically hold constant the effects of confounding variables in nonexperimental research.Slide9
Why NOT use Multivariate Stats?
You may be able adequately to address 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.Slide10
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.Slide11
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
plaintiff.Slide12
Logit AnalysisThis is a special case.
One variable is identified as dependent.
We are interested only in effects that involve the dependent variable.Slide13
Earlier ResearchPhysically 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 ?Slide14
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.Slide15
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.Slide16
Experiment 2 (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.Slide17
ConclusionsWhen 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.