Categorical Data Analysis Independent Explanatory Variable is Categorical

Categorical Data Analysis Independent (Explanatory) Variable is Categorical (Nominal or Ordinal) Dependent (Response) Variable is Categorical (Nominal or Ordinal) Special Cases: 2 x 2 (Each variable has 2 levels) Nominal/Nominal Nominal/Ordinal Ordinal/Ordinal

Contingency Tables representing all combinations of levels of explanatory and response variables Numbers in table represent Counts of the number of cases in each cell Row and column totals are called Marginal counts

Example – EMT Assessment of Kids Explanatory Variable – Assessment Child Age (Infant, Age Acc Inac Tot Toddler, Pre-school, Inf 168 73 241 School-age, Adolescent) Tod 230 73 303 Response Variable – Pre 254 53 307 EMT Assessment Sch 379 58 437 (Accurate, Ado 652 124 776 Inaccurate) Tot 1683 381 2064 Source: Foltin, et al (2002)

2 x 2 Tables Each variable has 2 levels Explanatory Variable – Groups (Typically based on demographics, exposure, or Trt) Response Variable – Outcome (Typically presence or absence of a characteristic) Measures of association Relative Risk (Prospective Studies) Odds Ratio (Prospective or Retrospective) Absolute Risk (Prospective Studies)

2 x 2 Tables - Notation Outcome Present Outcome Absent Group Total Group 1 n 12 n 1. Group 2 n 21 n 22 n 2. Outcome Total n. 1 n. 2 n. .

Relative Risk Ratio of the probability that the outcome characteristic is present for one group, relative to the other Sample proportions with characteristic from groups 1 and 2:

Probability & Independence Joint probability Marginal probability Conditional probability Sensitivity = P(+ | disease) Specificity = P( - | no disease) Independence of X and Y 7