Multivariate by changcheng2


									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
• Some call it univariate, as in “univariate
  ANOVA.” Here the focus is on how many
  comparison variables there are (only one
• If there were more than one Y, they would
  call it MANOVA and consider it
    Independent and Dependent
• 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, though 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
• In this case, there are no assumptions.
• If you use 2, t, or F, then there are
 Rank Data/Scale of Measurement
• Only God knows if your data are interval
  rather than merely ordinal, and she is not
• Ordinal data may be normally distributed.
• Interval data may not be normally
• Ranks are not normally distributed, but
  may be close enough to normal.
     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
 Why NOT use Multivariate Stats?
• You may be able adequate to address
  your research question with more simple
• 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
   Multidimensional Contingency
           Table Analysis
• Chapter 17 in Howell.
• Have three or more dimensions in the
  contingency table. All variables are
• Moore, Wuensch, Hedges, & Castellow
• Simulated civil case, sexual harassment.
• Female plaintiff, male defendant.
              The Design
• Physical attractiveness (PA) of defendant,
• Social desirability (SD) of defendant,
• Sex/gender of mock juror.
• Verdict recommended by juror
• Experiment 2: manipulated PA and SD of
            Logit Analysis
• This is a special case.
• One variable is identified as dependent.
• We are interested only in effects that
  involve the dependent variable.
• In second experiment the PA and SD of
  the plaintiff were manipulated.
          Earlier Research
• Physically attractive litigants are better
  treated by the jurors. No SD 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 though 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.
• When jurors have no relevant info on SD,
  they infer that the beautiful are good, and
  that affects their verdicts.
• When juror do have relevant info on SD,
  the PA of the litigants is of little

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