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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

Pulse Rates If we use the data given in Exercise 1 with two-way analysis of variance, we get the accompanying display. What do you conclude?

Empty Stomachs. In the publication "How Often Do Fishes 'Run on Empty'?' (Ecology, Vol. 83, No 8, Pp. 2145-2151), D. Arrington et al. examined almost 37,000fish of 254 species from the waters of Africa, South and Central America, and North America to determine the percentage of fish with empty stomachs. The fish were classified as piscivores (fish-eating), invertivores (invertibrateeating), omnivores (anything-eating) and algivores/detritivores (eating algae and other organic matter). For those fish in African waters, the data on the WeissStats site give the proportions of each species of fish with empty stomachs. At the 1% significance level, do the data provide sufficient evidence to conclude that a difference exists in the mean percentages of fish with empty stomachs among the four different types of feeders?

In Exercises 5–16, use analysis of variance for the indicated test.

Triathlon Times Jeff Parent is a statistics instructor who participates in triathlons. Listed below are times (in minutes and seconds) he recorded while riding a bicycle for five stages through each mile of a 3-mile loop. Use a 0.05 significance level to test the claim that it takes the same time to ride each of the miles. Does one of the miles appear to have a hill?

Mile 1

3:15

3:24

3:23

3:22

3:21

Mile 2

3:19

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3:21

3:17

3:19

Mile 3

3:34

3:31

3:29

3:31

3:29

Suppose that a one-way ANOVA is being performed to compare the means of three populations and that the sample sizes are 10,12 , and 15. Determine the degrees of freedom for the F-statistic.

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