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Follow the three R’s: Respect for self, Respect for others

Follow the three R’s: Respect for self, Respect for others and Responsibility for all your actions. Categorical Data Analysis. Chapter 1: Introduction Chapter 2: Two Way Tables. The Role of a Variable. Explanatory/predictor/independent variable Response/outcome/dependent variable

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Follow the three R’s: Respect for self, Respect for others

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  1. Follow the three R’s: Respect for self, Respect for others and Responsibility for all your actions

  2. Categorical Data Analysis Chapter 1: Introduction Chapter 2: Two Way Tables

  3. The Role of a Variable • Explanatory/predictor/independent variable • Response/outcome/dependent variable Q: Will women smoking during pregnancy have higher probability of miscarriage?

  4. Statistical Tools vs. Variable Types

  5. Distributions for Categorical Data • Binomial data • When the sample size n is fixed and the response per subject is binary • Multinomial data • When the sample size n is fixed and the response per subject is multinary • Poisson data • When the sample size n is not fixed and the response per subject is binary/multinary • Poisson model conditional on a given n is Binomial/ Multinomial model (Sec. 1.2.5)

  6. Distributions for Categorical Data • These models have overdispersion problem because they assume all subjects having the same probability of responding (from the same population) and ignore the covariates

  7. Review: Maximum Likelihood Inference Method • Likelihood functions • MLE (maximum likelihood estimate) • Asymptotical distribution of mle • Wald inference (test and confidence interval) • Example: binomial data

  8. Two-Way Tables • A table summarizes two categorical variables • Cells of a two-way table are frequency counts of combined outcomes of the two variables • Called IxJ tables for I rows and J columns Eg. Do you believe “afterlife”?

  9. Probability & Independence • Joint probability • Marginal probability • Conditional probability • Sensitivity = P(+ | disease) • Specificity = P( - | no disease) • Independence of X and Y

  10. Three Sampling Methods • Poisson sampling: no fixed total • Single multinomial sampling: fixed grand total • Independent multinomial sampling: fixed row or column totals

  11. Comparing Proportions in 2x2 Tables • Difference of proportions: pi1-pi2 • Relative risk: pi1/pi2 • Odds Ratio: odds1/odds2 odds1=pi1/(1-pi1) odds2=pi2/(1-pi2)

  12. More on Odds Ratio • Properties • Inference • Relationship to relative risk

  13. Comparing Proportions in stratified 2x2 Tables • Find the “conditional odds rations” describing the partial association in stratified 2x2 tables • Marginal vs. conditional independence • Homogeneous association • Same idea applying to IxJ tables

  14. Table 2.7

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