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Unformatted text preview: STA 3024 Introduction to Statistics 2 Chapter 4: Analysis of Variance (ANOVA) As stated in chapter 3, the table below outline the direction we are heading to Table 1: Methods to Investigate the Association between Variables Explanatory Variable(s) Response Variable Method Chapter 3 Categorical Categorical Contingency Tables Chapter 4 Categorical Quantitative Analysis of Variance (ANOVA) Chapter 5 and 6 Quantitative Quantitative Regression Analysis Quantitative Categorical (not discussed) Now, recall from chapter 3, we looked at the case where the two variables are both categorical. For example, we might ask subjects one question in which they identify their race (black/white/asian/hispanic/other), and we might ask another question in which they describe their political view (republican/democrat/independence). Recall the test for inde- pendence does not care which one is the response variable or explanatory variable. This chapter deals with a different scenerio where the explanatory variable is categorical and the response variable is quantitative. For example, we are interested in the amount of time it takes for a person to react to different get-your-attention sounds. Different get-your-attention sounds (siren, ice-cream jingles, crazy frog, wake-up alarm) are clearly categorical. The reaction time recorded by second is clearly quantitative. Instead of Analysis of Variance or ANOVA, a better tittle for this chapter might be Testing for Equality of Three or More Population Means. True, the latter title might not be catchy, but it does a better job decribing the objective of this chapter. From chapter 2, we encountered methods to compare means from two populations; however, those methods do not apply when three or more means are involved. Instead of referring to the main objective of testing for equal means, the term analysis of variance refers to the method we use, which is based on the analysis of sample variances. Analysis of variance (ANOVA) is a method of testing the equality of three or more population means by analyzing sample variances. Recall that a categorical explanatory variable is also called a factor or a treatment. The simplest form of ANOVA, one-way ANOVA, uses one factor/treatment and one response variable. Well also study a more complicated setup, two-way ANOVA, which uses two factors/treatments instead. This chapter corresponds to Chapter 14 of our textbook. Warning: The chapter will frequently make use of the notation . If you are not quite comfortable with , please read the Appendix at the end of the chapter for a review. 1 PART I - ONE-WAY ANOVA 1.1 Background and Notations Let the categorical explanatory variable has g number of groups/categories. Let the response variable be quatitative; that is, we can find the mean for each group, and the total mean for the whole sample....
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