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Multivariate Statistics An Introduction & Multidimensional Contingency Tables

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What Are Multivariate Stats? Univariate = one variable (mean) Bivariate = two variables (Pearson r) Multivariate = three or more variables simultaneously analyzed

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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Logit Analysis This is a special case. One variable is identified as dependent. We are interested only in effects that involve the dependent variable.

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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 ?

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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.

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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.

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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.

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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.

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