# 32 - Chapter 3 Association Contingency Correlation and...

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Chapter 3 Association: Contingency, Correlation, and Regression Section 3.1 How Can We Explore the Association between Two Categorical Variables?

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Learning Objectives 1. Identify variable type: Response or Explanatory 2. Define Association 3. Contingency tables 4. Calculate proportions and conditional proportions
Learning Objective 1: Response and Explanatory variables Response variable (Dependent Variable) the outcome variable on which comparisons are made Explanatory variable (Independent variable) defines the groups to be compared with respect to values on the response variable Example: Response/Explanatory Blood alcohol level/# of beers consumed Grade on test/Amount of study time Yield of corn per bushel/Amount of rainfall

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Learning Objective 2: Association The main purpose of data analysis with two variables is to investigate whether there is an association and to describe that association An association exists between two variables if a particular value for one variable is more likely to occur with certain values of the other variable
Learning Objective 3: Contingency Table A contingency table: Displays two categorical variables The rows list the categories of one variable The columns list the categories of the other variable Entries in the table are frequencies

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Learning Objective 3: Contingency Table What is the response variable? What is the explanatory variable?
Learning Objective 4: Calculate proportions and conditional proportions

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Learning Objective 4: Calculate proportions and conditional proportions What proportion of organic foods contain pesticides? What proportion of conventionally grown foods contain pesticides? What proportion of all sampled items contain pesticide residuals?
Learning Objective 4: Calculate proportions and conditional proportions Use side by side bar charts to show conditional proportions Allows for easy comparison of the explanatory variable with respect to the response variable

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Learning Objective 4: Calculate proportions and conditional proportions If there was no association between organic and conventional foods, then the proportions for the response variable categories would be the same for each food type
Chapter 3 Association: Contingency, Correlation, and Regression Section 3.2 How Can We Explore the Association between Two Quantitative Variables?

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Learning Objectives: 1. Constructing scatterplots 2. Interpreting a scatterplot 3. Correlation 4. Calculating correlation
Learning Objective 1: Scatterplot Graphical display of relationship between two quantitative variables: Horizontal Axis: Explanatory variable , x Vertical Axis: Response variable , y

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Learning Objective 1: Internet Usage and Gross National Product (GDP) Data Set INTERNET GDP INTERNET GDP Algeria 0.65 6.09 Japan 38.42 25.13 Argentina 10.08 11.32 Malaysia 27.31 8.75 Australia 37.14 25.37 Mexico 3.62 8.43 Austria 38.7 26.73 Netherlands 49.05 27.19 Belgium 31.04 25.52 New Zealand 46.12 19.16 Brazil 4.66 7.36 Nigeria 0.1 0.85 Canada 46.66 27.13 Norway 46.38 29.62 Chile 20.14 9.19 Pakistan 0.34 1.89 China 2.57 4.02 Philippines 2.56 3.84 Denmark 42.95 29
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## This note was uploaded on 08/01/2011 for the course STAT 101 taught by Professor Thomas during the Spring '11 term at Penn State.

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32 - Chapter 3 Association Contingency Correlation and...

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