Statistics for Business and Economics

David R. Anderson, Dennis J. Sweeney, Thomas A. Williams

ISBN #9780324365054

10th Edition

999 Questions

39,032 Students Helped

Homework Questions

Summary

Learning Objectives

Key Concepts

Example Problems

Explanations

Common Mistakes

Summary

This section illustrates how experimental design and analysis of variance (ANOVA) are used to test the equality of population means across multiple treatments. Key concepts include partitioning total variance into between-treatments and within-treatments components, computing F statistics to test hypotheses, and using multiple comparison procedures like Fisher’s LSD to pinpoint specific group differences. Understanding these ideas helps in designing robust experiments and accurately interpreting statistical results.

Learning Objectives

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Example Problems

Example 1

The following data are from a completely randomized design. a. Compute the sum of squares between treatments. b. Compute the mean square between treatments. c. Compute the sum of squares due to error. d. Compute the mean square due to error. e. Set up the ANOVA table for this problem. f. $\quad$ At the $\alpha=.05$ level of significance, test whether the means for the three treatments are equal.

Example 2

In a completely randomized design, seven experimental units were used for each of the five levels of the factor. Complete the following ANOVA table.

Example 3

Refer to exercise 2 a. What hypotheses are implied in this problem? b. $\quad$ At the $\alpha=.05$ level of significance, can we reject the null hypothesis in part (a)? Explain.

Example 4

In an experiment designed to test the output levels of three different treatments, the following results were obtained: $\mathrm{SST}=400, \mathrm{SSTR}=150, n_{T}=19 .$ Set up the ANOVA table and test for any significant difference between the mean output levels of the three treatments. Use $\alpha=.05$

Example 5

In a completely randomized design, 12 experimental units were used for the first treatment, 15 for the second treatment, and 20 for the third treatment. Complete the following analysis of variance. At a .05 level of significance, is there a significant difference between the treatments?