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Chapter 12: Q6CQQ (page 566)

One-Way ANOVA In general, what is one-way analysis of variance used for?

Short Answer

Expert verified

The one-way analysis of variance is used to test the difference in the means of three or more samples that are categorized under one factor.

Step by step solution

01

Given information

An analysis of variance test is conducted to test the difference in the sample means.

02

Describe the one-way analysis of variance

In the one-way analysis of variance, the sample values are categorized on only one factor/variable.

In a one-way analysis of variance test, the difference between more than two sample means is required to be tested.

Thus, the hypotheses to be tested are stated as follows.

  • The null hypothesis states that there is no difference in the sample means.
  • The alternative hypothesis states that at least one sample mean is different from the others.

Thus, the test is used for the comparison of three or more group means.

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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?

Estimating Length Given below is a Minitab display resulting from two-way analysis of variance with sample data consisting of 18 different student visual estimates of the length of a classroom. The values are categorized according to sex and major (math, business, liberal arts). What do you conclude about an interaction between sex and major?

Bonferroni Test Shown below are weights (kg) of poplar trees obtained from trees planted in a rich and moist region. The trees were given different treatments identified in the table below. The data are from a study conducted by researchers at Pennsylvania State University and were provided by Minitab, Inc. Also shown are partial results from using the Bonferroni test with the sample data.

No Treatment

Fertilizer

Irrigation

Fertilizer and Irrigation

1.21

0.94

0.07

0.85

0.57

0.87

0.66

1.78

0.56

0.46

0.10

1.47

0.13

0.58

0.82

2.25

1.30

1.03

0.94

1.64

  1. Use a 0.05 significance level to test the claim that the different treatments result in the same mean weight.
  1. What do the displayed Bonferroni SPSS results tell us?
  1. Use the Bonferroni test procedure with a 0.05 significance level to test for a significant difference between the mean amount of the irrigation treatment group and the group treated with both fertilizer and irrigation. Identify the test statistic and either the P-value or critical values. What do the results indicate?

Cola Weights The displayed results from Exercise 1 are from one-way analysis of variance. What is it about this test that characterizes it as one-way analysis of variance instead of two-way analysis of variance?
See all solutions

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