# One-Way Analysis of Variance (ANOVA)

• Thomas J. Quirk
Chapter

## Abstract

So far in this book, you have learned how to test for the difference within one group of data between the mean of the group and the hypothesized population mean for the data using either the 95% confidence interval about the mean (Chap. 3 of this book) or the one-group t-test of the mean (Chap. 4 of this book). You have also learned how to test for the difference between the means for two groups of people to determine if this difference was a “significant” difference (Chap. 5 of this book). In this chapter, you will learn how to test for the difference between groups on a single variable when you have three or more groups of data. A practical business problem is presented that walks you through the Excel steps needed to generate the output for a one-way ANOVA test. You will learn how to interpret the Summary Output table correctly, and how to test the hypotheses comparing the population means of the three or more groups to see if they are “significantly different from each other.” If this overall ANOVA test produces a significant result, you will learn how to test the hypotheses comparing any two groups using an ANOVA t-test formula. This formula is presented, explained, and a practical business example is used delineating the five steps needed to perform this test using a calculator. Then, the Excel steps for using this formula are presented and explained. Three practice problems are given at the end of the chapter to test your Excel skills, and the answers to these problems appear in Chap. 9 of this book. An additional practice problem is presented in the Practice Test given in Chap. 10 along with its answer in Chap. 11 of this book.

Income Crest

### References

1. Black, K. (2010). Business statistics: For contemporary decision making (6th ed.). Hoboken, NJ: Wiley.Google Scholar
2. Weiers, R. M. (2011). Introduction to business statistics (7th ed.). Mason, OH: South-Western Cengage Learning.Google Scholar