# Unit 4: Contingency Tables & Simple Logistic Regression: Inference in Case CC and QC

## Learning Objectives

Contingency Table Methods for Binary Outcomes

• Apply contingency tables for binary outcomes with binary or multi-level predictors
• Identify the appropriate conditional percentages to compare to answer specific research questions.
• Conduct the appropriate chi-square test for association or when appropriate use Fisher’s exact test.
• Calculate and interpret measures of association for binary outcomes
• Excess Risk (or Risk Difference)
• Relative Risk
• Odds Ratio
• Discuss issues related to the three measures of association for binary outcomes.

Logistic Regression using One Predictor

• Use LOG rules for powers and division appropriately as needed to work with logistic models.
• Discuss the reasons the logistic model is preferred for modeling probabilities.
• Discuss the benefit of the logistic model that it can be rewritten in terms of a linear model using an appropriate LOGIT transformation.
• Use the logistic model to predict probabilities or LOG-ODDS.
• State the assumptions of the logistic regression model.
• Derive and appropriately interpret the log-odds-ratio and odds-ratio for comparing levels of a categorical predictor to the reference group.
• Derive and appropriately interpret the log-odds-ratio and odds-ratio for a one-unit increase or a c-unit increase for a continuous predictor.
• Appropriately use SAS output to conduct logistic regression analysis for one predictor and multiple predictors, possibly including interactions.
• Construct confidence intervals for parameter estimates and odd-ratios by hand for comparisons to a reference group for categorical predictors.
• Construct confidence intervals for parameter estimates and odd-ratios by hand for a one-unit or c-unit increase in a continuous predictor.
• Be able to find odd-ratio and confidence intervals in the reverse direction of comparisons given in software output by taking the reciprocal of the values in the output.
• Use contrast and oddsratio statements to test and estimate complex comparisons.
• Appropriately use percent increase or percent decrease interpretations for odd-ratios.

The following lessons from Penn State STAT 501 are linked in the materials as support materials for Unit 4. Our videos will be the primary instruction for Unit 4 and Unit 5.