STATS 111/202 Lecture 2 Sevan Koko Gulesserian University of California, Irvine 1 / 34

Statistical Modeling We will now expand the scenario of a one way table (having only a single categorical response withJ≥2 categories) to account for a single categorical explanatory variable. This type of data (a single categorical response and a single categorical explanatory variable) is commonly represented using a two way table. The inference goal of such types of data is to investigate if there is a statistically significant relationship between the response and the categorical explanatory variable. Examples: Response variable is if a subject is diabetic yes/no and explanatory variable is if the subject has high blood pressure (>120) yes/no. 2 / 34

Statistical Modeling: 2 Way Tables Let us begin with a response ,Y, having two categories (1 and 0, to signify yes and no respectively) and similarly for an explanatory variable X. The following is a general two way table with binary variables. Y=1Y=0Total X=1n11n12n 1+ X=0n21n22n 2+ Totaln+1n+2 n 3 / 34