chapter3 - CHAPTER 3: EXPLORING RELATIONSHIPS 3.1 Response...

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CHAPTER 3: EXPLORING RELATIONSHIPS 3.1 Response and Explanatory Variables What is the nature of the relationship? Which variable influences which? X Y (X influences Y) X = explanatory variable, Y = response variable. Blood Pressure Age Coronary heart disease Pet ownership 3.2 The Association Between Two Categorical Variables Example 1: Survival and Pet Ownership A study examined the relationship between survival of patients with coronary heart disease (CHD) and pet ownership. Each of 92 patients was classified as having a pet or not and by whether they survived for 1 year. Survival (categorical variable, categories: alive, dead) Pet ownership (categorical variable, categories: pet, no pet) 1
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Pet Ownership Patient Status after 1 year No Yes Alive 28 50 Dead 11 3 Pet Ownership Total Patient Status No Yes Alive 28 50 Dead 11 3 Total Contingency table for patient status and pet ownership Survival rate for patients without pets: Survival rate for patients with pets: Conditional proportions (under condition of survival) Survival Rate No pet pet 2
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Example 2: Smoking by students and their parents How are the smoking habits of students related to their parents’ smoking? Student Parents Smokes Does not smoke Both parents smoke 400 1380 One parent smokes 416 1823 Neither parent smokes 188 1168 Parents’ smoking status (categorical variable, categories: both, one, neither) Student’s smoking status (categorical variable, categories: smokes, does not smoke) Student Total Parents Smokes Does not smoke Both smoke 400 1380 One smokes 416 1823 Neither smokes 188 1168 Total Percentage of students who smoke (both parents smoke): Percentage of students who smoke (on parent smokes): Percentage of students who smoke (neither parent smokes): 3
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Percent of students who smoke both one neither In general, we define contingency table for two categorical variables A and B as follows: B Total B B 1 B 2 B j B c A 1 A 2 A i A A r Total n Observed count of observations falling into A i and B j Explore the relationship by examining the conditional proportions. 4
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3.3 Association Between Two Quantatative Variables X, Y - two quantitative variables. Problem: Is there a relationship between X and Y?
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This note was uploaded on 04/10/2008 for the course STAT 151 taught by Professor Henrykkolacz during the Fall '07 term at University of Alberta.

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chapter3 - CHAPTER 3: EXPLORING RELATIONSHIPS 3.1 Response...

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