# Which type of test of means is it?

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STAT 301 March 10, 2014 Homework #7 Due Wednesday Lab #8 Friday - will be on Blackboard soon and must be turned in by Friday either on Blackboard or in lab as usual. Gradient #2 writing is Monday 3/24
Which type of test of means is it? Review insurance records for dollar amount paid after fire damage in houses equipped with a
fire extinguisher vs. houses without one. Was there a difference in the average dollar amount paid?
One-Way ANOVA: One-Way Analysis of Variance (Chpt. 12) © 2011 W.H. Freeman and Company
4 Introduction The two sample t procedures of Chapter 7 compared the means of two populations or the mean responses to two treatments in an experiment. In this chapter we’ll compare any number of means using Analysis of Variance (ANOVA) . Note: We are comparing means even though the procedure is Analysis of Variance.
The idea of ANOVA A factor is a variable that can take one of several levels, one for each treatment group. An experiment has a one-way or completely randomized design if several levels of one factor are being studied and the individuals are randomly assigned to its levels. (There is only one way to group the data . ) Example: Which of four advertising offers mailed to sample households produces the highest sales? Will a lower price in a plain mailing draw more sales on average than a higher price in a fancy brochure? Analyzing the effect of price and layout together requires two-way ANOVA. Analysis of variance ( ANOVA ) is the technique used to determine whether more than two population means are equal. One-way ANOVA is used for completely randomized, one-way designs.
6 The sample means for the three samples are the same for each set. The variation among sample means for (a) is identical to (b). The variation among the individuals within the three samples is much less for (b). CONCLUSION: the samples in (b) contain a larger amount of variation among the sample means relative to the amount of variation within the samples, so ANOVA will find more significant differences among the means in (b) assuming equal sample sizes here for (a) and (b). Note: larger samples will find more significant differences. The Idea of ANOVA
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