lecture_04 - Two-Way Contingency Tables Contingency Tables...

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Two-Way Contingency Tables
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    Contingency Tables -  Introduction Contingency tables are common ways to  summarize categorical / qualitative data. Cells of the table contain frequency counts of  outcomes. In other words contingency table is a  table of counts. A simplest form of contingency table is a     2 x 2 table.
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  Contingency Tables -  Introduction A two-dimensional contingency table is formed by  classifying subjects by two variables. One variable determines the row categories, the other  variable defines the column categories. The combination of row and column categories are called  cells. Examples include classifying subjects by sex (male/female)  and smoking status (current/former/never) or by classifying  subjects by smoking status (yes/no) and whether the person  has a CHD (yes/no).
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      2 x 2 Contingency Table Example: Following table classifies a sample of 1091 Americans who were asked for their belief in  afterlife.                           Belief in Afterlife Gender Yes No or Undecided Females 435 147 Males 374 134
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2 x 2 Contingency Table                              Belief in Afterlife Gender Yes No or Undecided Females 435 147 Males 374 134 In the above example there are 2 categorical variables: GENDER Female, Male BELIEF – Yes, No There are 2 rows and 2 columns. Therefore it is a 2 x 2 table.
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      Objective of contingency tables Objective is to see if there is an association  between the categorical variables. In addition, we may be interested in the strength of  the association. For the “Belief in Afterlife” example: Is one sex more likely than the other to believe in  afterlife? Is belief in afterlife independent of  gender?
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            Example 2   Categorizing patients by their favorable or unfavorable  response to two different drugs. The objective is to see if there is any association between drugs  and their favourable outcomes. Is drug A more favourable than drug B? Drug Favorable Unfavorable A 16 48 B 40 20
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        Example 3  Death sentence by race of defendant for 147 penalty trials. The objective is to see if there is any association between  death sentence and race of the defendant. Is death sentence more likely for a black than life sentence? Blacks Nonblacks DEATH 28 22 LIFE 45 52
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    Probability Structure Categorical data consist of frequency counts of  observations occurring in the response categories.  Let X and Y denote two categorical variables X having I  levels and Y having J levels.  We can have the IJ possible combinations of outcomes in a 
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