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Chapter 12: Q7CQQ (page 566)

One vs. Two What is the fundamental difference between one-way analysis of variance and two-way analysis of variance?

Short Answer

Expert verified

The fundamental difference between the one-way analysis and the two-way analysis of variance is that in the one-way analysis of variance, the sample values are categorized on the basis of only one factor, while in the two-way analysis of variance, the sample values are categorized based on two factors.

Step by step solution

01

Given information

The analysis of variance test is compared based on two categories: one-way and two-way.

02

One-way analysis of variance vs. two-way analysis of variance

The analysis of variance is a test conducted for testing sample means across three or more groups.The categorization is based on the number of factors used in the study.

In a one-way analysis of variance test, the difference in the sample means is needed to be tested when the sample values vary across one factor.

In a two-way analysis of variance, the sample values vary across two factors. The difference in the sample means is computed for factor 1 and factor 2, and the interaction effect between the two factors is considered a separate factor.

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Most popular questions from this chapter

Cola Weights Data Set 26 鈥楥ola Weights and Volumes鈥� in Appendix B lists the weights (lb) of the contents of cans of cola from four different samples: (1) regular Coke, (2) diet Coke, (3) regular Pepsi, and (4) diet Pepsi. The results from the analysis of variance are shown on the top of the next page. What is the null hypothesis for this analysis of variance test? Based on the displayed results, what should you conclude about H0? What do you conclude about the equality of the mean weights of the four samples?

Balanced Design Does the table given in Exercise 1 constitute a balanced design? Why or why not?

The heights (cm) in the following table are from Data Set 1 鈥淏ody Data鈥� in Appendix B. Results from two-way analysis of variance are also shown. Use the displayed results and use a 0.05 significance level. What do you conclude?


Female

Male

18-29

161.2

170.2

162.9

155.5

168

153.3

152

154.9

157.4

159.5

172.8

178.7

183.1

175.9

161.8

177.5

170.5

180.1

178.6

30-49

169.1

170.6

171.1

159.6

169.8

169.5

156.5

164

164.8

155

170.1

165.4

178.5

168.5

180.3

178.2

174.4

174.6

162.8

50-80

146.7

160.9

163.3

176.1

163.1

151.6

164.7

153.3

160.3

134.5

181.9

166.6

171.7

170

169.1

182.9

176.3

166.7

166.3

Tukey Test

A display of the Bonferroni test results from Table 12-1 (which is part ofthe Chapter Problem) is provided on page 577. Shown on the top of the next page is the SPSS-generated display of results from the Tukey test using the same data. Compare the Tukey test results to those from the Bonferroni test.

In Exercises 1鈥�5, refer to the following list of departure delay times (min) of American Airline flights from JFK airport in New York to LAX airport in Los Angeles. Assume that the data are samples randomly selected from larger populations.

Flight 3

22

-11

7

0

-5

3

-8

8

Flight 19

19

-4

-5

-1

-4

73

0

1

Flight 21

18

60

142

-1

-11

-1

47

13

Exploring the Data Include appropriate units in all answers.

a. Find the mean for each of the three flights.

b. Find the standard deviation for each of the three flights.

c. Find the variance for each of the three flights.

d. Are there any obvious outliers?

e. What is the level of measurement of the data (nominal, ordinal, interval, ratio)?
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