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# chapter3small - Section 3.1 How Can We Explore the...

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Unformatted text preview: Section 3.1 How Can We Explore the Association between Two Categorical Variables? May 11, 2009 1 3 Association: Contingency, Correlation, and Regression When comparing two variables, sometimes one variable (the explanatory variable) can be used to help predict the value of another variable (the response variable). Often we are interested in the association (i.e., a relationship) between two or more variables. Example: * A person’s height, weight, blood pressure, cholesterol level, body mass index, age, gender, incidence of heart attack. * A person’s height, weight, blood pressure, cholesterol level, body mass index, age, gender, incidence of heart attack. Example: For the following pairs of variables, which is the explanatory variable, and which is the response variable? (a) number of years of education and income (b) blood pressure (systolic) and weight (c) height of sons and height of fathers (d) score on midterm exam and score on final exam (e) score on SAT and final GPA in college (f) deficit spending and interest rates (g) temperature and ozone in atmosphere 3.1 How Can We Explore the Association between Two Categorical Variables? Set up a contingency table , for comparing two categorical variables. Section 3.1 How Can We Explore the Association between Two Categorical Variables? May 11, 2009 2 Within a contingency table, we can determine conditional proportions ; i.e., the proportion of the time that a variable takes on a particular value, conditional on some value of the other variable. Example: Consider the following contingency table regarding the gender of an un- born baby (The data are hypothetical but are somewhat consistent with untrasounds from the 1990’s.): Ultrasound Ultrasound Predicted Predicted Female Male Actual gender is female 432 48 Actual gender is male 130 390 Based on the above contingency table: (a) What proportion of babies are female , given that the ultrasound predicted that the baby would be female ? * 432 / 562 = 0 . 769 * 432 / 562 = 0 . 769 (b) What proportion of babies are male , given that the ultrasound predicted that the baby would be male ? * 390 / 438 = 0 . 890 * 390 / 438 = 0 . 890 (c) Is the ultrasound equally reliable for predicting gender for boys and for girls? * No, an ultrasound predicting a boy is more likely to be correct than an ultra- sound predicting a girl . * No, an ultrasound predicting a boy is more likely to be correct than an ultra- sound predicting a girl . Section 3.2 How Can We Explore the Association between Two Quantitative Variables? May 11, 2009 3 3.2 How Can We Explore the Association between Two Quantitative Variables?...
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chapter3small - Section 3.1 How Can We Explore the...

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