Log out Go to App
Go to App

Learning Materials

Features

Discover

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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Cola Weights Identify the value of the test statistic in the display included with Exercise 1. In general, do larger test statistics result in larger P-values, smaller P-values, or P-values that are unrelated to the value of the test statistic?

Interaction

a. What is an interaction between two factors?

b. In general, when using two-way analysis of variance, if we find that there is an interaction effect, how does that affect the procedure?

c. Shown below is an interaction graph constructed from the data in Exercise 1. What does the graph suggest?

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.

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?

Car Crash Tests Data Set 19 “Car Crash Tests” in Appendix B lists results from car crash tests. The data set includes crash test loads (pounds) on the left femur and right femur. When those loads are partitioned into the three car size categories of small, midsize, and large, the two-way analysis of results from XLSTAT are as shown below. (The row factor of femur has the two values of left femur and right femur, and the column factor of size has the three values of small, midsize, and large.) Use a 0.05 significance level to apply the methods of two-way analysis of variance. What do you conclude?
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Pure Maths

Read Explanation

Discrete Mathematics

Read Explanation

Applied Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free