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Chapter 12: Q2BSC (page 566)

Two-Way ANOVA If we have a goal of using the data described in Exercise 1 to (1) determine whether age bracket has an effect on pulse rates and (2) to determine whether gender has an effect on pulse rates, should we use one-way analysis of variance for the two individual tests? Why or why not?

Short Answer

Expert verified

No, one-way analysis of variance should not be used to check the effects of gender and age separately.The result will not be the same as obtained after applying a two-way analysis of variance.

Step by step solution

01

Given information

Data are given on the pulse rates of men and women. It is further classified according to three different age groups.

02

One-way and two-way analysis of variance

A one-way ANOVA explains the difference among the three or more groups of single factor in terms of their means.

A two-way analysis of variance is conducted for a set of data that consists of values that differ on two different categories.

It helps assess the difference in the mean values of individual factors; that is, one is the row category, and the other is the column category. This analysis also includes the difference in the mean values due to the combined effect or interaction effect between row and column categories.

03

Difference between the one-way ANOVA and two-way ANOVA

When a two-way analysis of variance is conducted, the interaction effect is also considered.

But, when a one-way analysis of variance is conducted twice, the interaction effect is not considered,so the results are different.

Therefore, a two-way analysis of variance cannot be replaced with a one-way analysis of variance conducted twice.

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Most popular questions from this chapter

Confidence Interval Use the departure delay times for Flight 3 and construct a 95% confidence interval estimate of the population mean. Write a brief statement that interprets the confidence interval.

In Exercises 1–4, use the following listed arrival delay times (minutes) for American Airline flights from New York to Los Angeles. Negative values correspond to flights that arrived early. Also shown are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different flights have the same mean arrival delay time.

Flight 1

-32

-25

-26

-6

5

-15

-17

-36

Flight 19

-5

-32

-13

-9

-19

49

-30

-23

Flight 21

-23

28

103

-19

-5

-46

13

-3

Why Not Test Two at a Time? Refer to the sample data given in Exercise 1. If we want to test for equality of the three means, why don’t we use three separate hypothesis tests for\({\mu _1} = {\mu _2},{\mu _1} = {\mu _3}\;and\;{\mu _2} = {\mu _3}\)?

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?

Normal Quantile Plot The accompanying normal quantile plot was obtained from the Flight 19 departure delay times. What does this graph tell us?

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