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Class 22

Class 22. Social Statistics (II). Class Outline. Review of the Elaboration Model Interpreting Regression Results Discussion of Readings Sex and Sports. X. Y. Z. X. Y. Z. X. Y. Z. Review of the Elaboration Model. 1. The 3 rd variable is an intervening variable. 2.

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Class 22

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  1. Class 22 Social Statistics (II)

  2. Class Outline • Review of the Elaboration Model • Interpreting Regression Results • Discussion of Readings • Sex and Sports

  3. X Y Z X Y Z X Y Z Review of the Elaboration Model 1. The 3rd variable is an intervening variable. 2. The 3rd variable is a confounding variable. 3. The 3rd variable interacts with the independent variable.

  4. Review of the Elaboration Model Babbie Chapter 15 • Extraneous variable = lurking variable = confounding variable • Suppressor variable • Distorter variable • Partial vs. zero-order relationship

  5. What is the Relationship Between Education and Vocabulary? education | mean(wordsum) 0 | 3.33333 1 | 2.375 2 | 3.48 3 | 3.04762 4 | 2.85556 5 | 3.22523 6 | 3.65753 7 | 4.06129 8 | 4.51555 9 | 4.40147 10 | 4.87015 11 | 4.88294 12 | 5.72973 13 | 6.1119 14 | 6.40381 15 | 6.69267 16 | 7.35741 17 | 7.59898 18 | 7.97003 19 | 8.2 20 | 8.33333 Means Table Bar Chart

  6. What is the Relationship Between Education and Vocabulary? -- Regression ------------------------------------------------------------------------------ wordsum | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .3589895.0043431 82.66 0.000.3504766 .3675023 _cons | 1.411986 .056832 24.84 0.000 1.300591 1.523381 ------------------------------------------------------------------------------ • Regression equation: wordsum = 1.412 + 0.359 * educ + e • The strength of association between the independent variable educ and the dependent variable wordsum is 0.359. • The slope of the fitted line with education on the X-axis and wordsum on the Y-axis is 0.359. • One year of education increases vocabulary score by 0.359 on average. • The average score for respondents with no schooling is 1.412, and that for respondents with 1 year’s education is 1.412+0.359, so on and so forth.

  7. t Statistic and p-Value • The S.E. of the coefficient 0.359 is 0.004. S.E. indicates how variable our estimate of a coefficient is. • t = coefficient/S.E. The larger the t, the more robust the result. • P-value is the probability of the observed relationship between the IV and the DV in the sample given that there is no such association in the population. A p-value smaller than 0.05 indicates a statistically significant relationship.

  8. Statistical and Substantive Significance • Substantivesignificance – estimated coefficient is strong, important and meaningful. • Statisticalsignificance – p-value is smaller than < 0.05, which means that the observed association between the IV and the DV is not due to sampling error. The larger the sample is, the more likely we will find statistical significance.

  9. Multiple Regression: Regression with More than One Independent Variables ------------------------------------------------------------------------------ wordsum | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- educ | .3610817 .0043441 83.12 0.000 .3525669 .3695965 sex | .2142668 .0266892 8.03 0.000 .1619537 .2665799 _cons | 1.048991 .0725545 14.46 0.000 .9067779 1.191203 ------------------------------------------------------------------------------ • Regression equation: wordsum = 1.412 + 0.359 * educ + 0.214 * sex + e (sex is coded 1=M, 2=F) • Interpretation: Holding sex constant, one year of education increases vocabulary score by 0.361 on average. Holding education constant, women on average score 0.214 higher on the vocabulary test than men do.

  10. Types of Regression Analysis • Linear regression analysis • Multiple regression analysis • Partial regression analysis • e.g., table 2 of the Intercohort Decline in Verbal Ability: Does it Exist? (Wilson and Gove 1999) • Nonlinear regression analysis • e.g., table 3 of Wilson and Gove (1999)

  11. Sex and Sports:Are Women Catching up?

  12. Sex and Sports:Comparing Progress Trajectories Bronze Medal Speeds in Olympics: 100m Sprint Speeds in 100M (m/s) 1896 2000 Men Women

  13. Sex and Sports • Why is it incorrect to extrapolate from historical data of world records (figures 1-7) and conclude that women will eventually surpass men in running and swimming? • Wainer et al. compared the trajectories of bronze medal performance for men and women over decades and extracted two parameters from the comparisons. What are the two parameters and what did they signify according to the authors? (p. 9) • The sex gap in performance in swimming appears to be smaller than that in running. What might be the physiological and social explanations for that?

  14. Sex and Sports • Find at least two criticisms of the Wainer et al. paper in Martin’s comment (p.16-17). • Find two places where Phillip Price (p.18-20) likes Wainer et al’s study. • Find two major criticisms of this study in Price’s comment.

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