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Association, Correlation and Regression

Association, Correlation and Regression. Bivariate association. Categorical/nominal variables Two way tables C 2 , phi ( f ) More than 2*2 way tables Cramer’s V Bar charts – side by side. C 2 < .000. Bivariate association – Ordinal variables. Ordinal variables Rank correlation

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Association, Correlation and Regression

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  1. Association, Correlation and Regression

  2. Bivariate association • Categorical/nominal variables • Two way tables • C2, • phi (f) • More than 2*2 way tables • Cramer’s V • Bar charts – side by side C2 < .000

  3. Bivariate association – Ordinal variables • Ordinal variables Rank correlation • Collapsed levels – income and expenditure groups • Gamma • Somer’s d • Kendal’s tau-b • Many levels – mothers’s and father-s education • Spearman rho s & tau-b take values 0 -1, with larger Values implying stronger association

  4. Continuous (interval/ratio) variables • Correlation Analysis • Scatter graph - two variables on same plot • Pearson’s r Coefficient of determination • R2 (r-square)

  5. bivariate regression • Correlation/regression coefficients (a & b) a is the intercept b is the slope • Predict “dependant” variable from “independent” variable • R-square

  6. beware

  7. Confidence intervals of regression lines

  8. Multivariate regression

  9. Partial correlation • Relationship between y and x depends on a third variable z • Juvenile sex ratio in India depends on female employment and kinship pattern (front page graph)

  10. Multiple regression of FMR on FLP and kinship 1. Correlation between fmr59 & flp 2. Partial Correlation Controlling for Kinship 3. Regression 5. and slope 4. controlling intercept of FLP Note that the slope of FLP declines from bivariate regression (3), through taking account of kinship intercept (4), but rises when slope interacts with kinship (5)

  11. Simple confounding What we see is FLP only has an effect on FMR in Kinship 1 (Indo-Aryan) districts; in the other districts FLP has no effect We can say that the effect of FLP on FMR is confounded with Kinship (although it is a bit more complicated than that)

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