1Class 22Social Statistics (II)Class Outline• Review of the Elaboration Model • Interpreting Regression Results• Discussion of Readings– Sex and SportsReview of the Elaboration ModelThe 3rdvariable is an intervening variable.The 3rdvariable is a confounding variable.The 3rdvariable interacts with the independent variable.XYZXYZXYZ1.2.3.2Review of the Elaboration ModelBabbie Chapter 15• Extraneous variable = lurking variable = confounding variable• Suppressor variable • Distorter variable• Partial vs. zero-order relationshipWhat is the Relationship Between Education and Vocabulary?education | mean(wordsum)0 | 3.333331 | 2.3752 | 3.483 | 3.047624 | 2.855565 | 3.225236 | 3.657537 | 4.061298 | 4.515559 | 4.4014710 | 4.8701511 | 4.8829412 | 5.7297313 | 6.111914 | 6.4038115 | 6.6926716 | 7.3574117 | 7.5989818 | 7.9700319 | 8.220 | 8.333330 2 4 6 8mean of wo rdsum0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20Mean Vocabulary Score by EducationMeans TableBar ChartWhat 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.3t 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.Statistical and Substantive Significance• Substantive significance – estimated coefficient is strong, important and meaningful.• Statistical significance – 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.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 .3695965sex | .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.4Types 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)Sex and Sports:Are Women Catching up?8 8.5 9 9.5 101900 1920 1940 1960 1980 2000yearmenspeed Fitted valueswomenspeed Fitted valuesOlympics Bronze Medal Speed in 100M SprintSex and Sports:Comparing Progress TrajectoriesMen Women20001896Speeds in 100M (m/s)Bronze Medal Speeds in Olympics: 100m Sprint5Sex 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?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
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