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Describing Bivariate Relationships

Describing Bivariate Relationships. 17.871 Spring 2006. Measures of association. Discrete data (Utts & Heckard, sect. 6.4) χ 2 Gamma, Beta, etc. Continuous or discrete data (Pearson) correlation coefficient (Spearman) rank-order correlation coefficient. Example I.

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Describing Bivariate Relationships

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  1. Describing Bivariate Relationships 17.871 Spring 2006

  2. Measures of association • Discrete data (Utts & Heckard, sect. 6.4) • χ2 • Gamma, Beta, etc. • Continuous or discrete data • (Pearson) correlation coefficient • (Spearman) rank-order correlation coefficient

  3. Example I • What is the relationship between religion and abortion sentiments? • The abortion scale: 1. BY LAW, ABORTION SHOULD NEVER BE PERMITTED. 2. THE LAW SHOULD PERMIT ABORTION ONLY IN CASE OF RAPE, INCEST, OR WHEN THE WOMAN'S LIFE IS IN DANGER. 3. THE LAW SHOULD PERMIT ABORTION FOR REASONS OTHER THAN RAPE, INCEST, OR DANGER TO THE WOMAN'S LIFE, BUT ONLY AFTER THE NEED FOR THE ABORTION HAS BEEN CLEARLY ESTABLISHED. 4. BY LAW, A WOMAN SHOULD ALWAYS BE ABLE TO OBTAIN AN ABORTION AS A MATTER OF PERSONAL CHOICE.

  4. Theoretical distribution of cells with abortion and religion independent

  5. Actual and theoretical distribution χ2=38.2

  6. Example II • What is the relationship between income and newspaper reading?

  7. Stylized relationship if newspaper reading increases with income

  8. Actual relationship between newspaper reading and income χ2=25.0, Gamma = +.16

  9. Example III • What is the relationship between Bush’s vote (by county) in 2000 and in 2004?

  10. 2004 Prez. Vote vs. 2000 Pres. Vote

  11. Subtract each observation from its mean x’=x-0.588 y’=y-0.609

  12. Covariance formula Cov(BushPct00,BushPct04) =0.014858

  13. Correlation formula Corr(BushPct00,BushPct04) =0.96 = c.f. Utts & Heckard p. 166

  14. Playing with the Utts & Heckard Correlation Applet

  15. Guessing Correlations Aplet http://www.stat.uiuc.edu/~stat100/java/guess/GCApplet.html

  16. Warning: • Correlation only measures linear relationship

  17. Anscombe’s Quartet r = .8164

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