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 with J 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=1 Y=0 Total X=1 n 11 n 12 n 1 + X=0 n 21 n 22 n 2 + Total n + 1 n + 2 n 3 / 34
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