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Unformatted text preview: Lesson 4: Relationships Between Categorical Variables Introduction In this lesson we will focus on the following different situations: 1. How to determine whether two categorical variables are related 2. How to compare two groups (categories of an explanatory variable) with regard to the risk of being in an "undesirable" category of a response variable Let's get started! Here is what you will learn in this lesson. Learning objectives for this lesson Upon completion of this lesson, you should be able to: Know what type of situations call for a chi-square analysis Begin to understand and apply the concept of "statistical significance" Calculate relative risk and odds ratio from a two-by-two table Explain the difference between relative risk and odds ratio better comprehend the difference between quantitative and qualitative variables 1. Determining whether two categorical variables are related The starting point for analyzing the relationship is to create a two-way table of counts. The rows are the categories of one variable and the columns are the categories of the second variable. We count how many observations are in each combination of row and column categories. When one variable is obviously the explanatory variable in the relationship, the convention is to use the explanatory variable to define the rows and the response variable to define the columns. This is not a hard and fast rule though. Example 1 : Students in our Stat 200 this semester we're asked how important religion is in your life (very important, fairly important, not important). A two-way table of counts for the relationship between religious importance and gender (female, male) is shown below. Fairly important Not important Very important All Female 56 32 39 127 Male 43 31 25 99 All 99 63 64 226 As an example of reading the table, 32 females said religion is "not important" in their own lives compared to 31 males. Fairly even! Example 2: Participants in the 2002 General Social Survey, a major national survey done every other year, were asked if they own a gun and whether they favor or oppose a law requiring all guns to be registered with local authorities. A two-way table of counts for these two variables is shown below. Rows indicate whether the person owns a gun or not. Owns Gun Favors Gun Law Opposes Gun Law All No 527 72 599 Yes 206 102 308 All 733 174 907 Percents for two-way tables Percents are more useful than counts for describing how two categorical variables are related. Counts are difficult to interpret, especially with unequal numbers of observations in the rows (and columns). Row Percents Example 1 Continued : The term "row percents" describes conditional percents that give the percents out of each row total that fall in the various column categories....
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This note was uploaded on 03/30/2008 for the course STAT 200 taught by Professor Barroso,joaor during the Spring '08 term at Pennsylvania State University, University Park.
- Spring '08