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Chapter 12: Q3BSC (page 566)

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?

Short Answer

Expert verified

a. The interaction effect among two factors is the effect upon the combination of both the factors. It is the effect of one factor over the other factor.

b. If two-way analysis of variance is applied, the hypothesis is set up to test the interaction effect first. If the interactioneffectcomes out to be significant,the individual effects of the factors cannot be considered separately.

c. Since the two lines are not parallel;there is an interaction effect between the factors age and gender.

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

Interaction effect

a.

An interaction effect is the effect of the two factors combined on the response variable.

.

It deals with the change in one factor caused to the effect of the other factor.

03

Two-way analysis of variance

b.

In a two-way analysis of variance, a null hypothesis is set up to test the significance of the interaction effect first.

If the null hypothesis is rejected, then the effects of one factor cannot be considered without the effect of the other factor;thus, the individual effects are not tested.

This is the major change in the procedure of two-way analysis of variance compared to the one-way analysis of variance.

04

Interpret the graph

c.

If the two lines in the interaction graph are far from being parallel, then there is an interaction between the two factors.

In the graph shown, it can be observed that the two lines are not parallel to each other.

Thus, it can be concluded that there is an interaction effect between age and gender.

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Most popular questions from this chapter

In Exercises 5鈥�8, use the following two control charts that result from testing batches of newly manufactured aircraft altimeters, with 100 in each batch. The original sample values are errors (in feet) obtained when the altimeters are tested in a pressure chamber that simulates an altitude of 6000 ft. The Federal Aviation Administration requires an error of no more than 40 ft at that altitude.

Is the process variation within statistical control? Why or why not?

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

In Exercises 1鈥�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鈥檛 we use three separate hypothesis tests for\({\mu _1} = {\mu _2},{\mu _1} = {\mu _3}\;and\;{\mu _2} = {\mu _3}\)?

Pages were randomly selected by the author from The Bear and the Dragon by Tom Clancy, Harry Potter and the Sorcerer鈥檚 Stone by J. K. Rowling, and War and Peace by Leo Tolstoy. The Flesch Reading Ease scores for those pages are listed below. Do the authors appear to have the same level of readability?

Clancy

58.2

73.4

73.1

64.4

72.7

89.2

43.9

76.3

76.4

78.9

69.4

72.9

Rowling

85.3

84.3

79.5

82.5

80.2

84.6

79.2

70.9

78.6

86.2

74.0

83.7

Tolstoy

69.4

64.2

71.4

71.6

68.5

51.9

72.2

74.4

52.8

58.4

65.4

73.6

Win 4 Lottery Shown below is a histogram of digits selected in California鈥檚 Win 4 lottery. Each drawing involves the random selection (with replacement) of four digits between 0 and 9 inclusive.

a. What is fundamentally wrong with the graph?

b. Does the display depict a normal distribution? Why or why not? What should be the shape of the histogram?

c. Identify the frequencies, then test the claim that the digits are selected from a population in which the digits are all equally likely. Is there a problem with the lottery?
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