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Chapter 13: Q5CQQ (page 597)

Foot Length , Height When analyzing the paired data in Exercise 4, are the P-values and conclusions from the nonparametric test and the parametric test always the same?

Short Answer

Expert verified

No, the p-values from the parametric and the nonparametric tests are not the same, but the conclusion from these tests may or may not vary.

Step by step solution

01

Given information

Data are given on two variables, “Foot Length(cm)” and “Height(cm)” of males.

02

Parametrictest vs. nonparamteric test

  • P-values

The p-values of a parametric and a nonparametric test are always different.

  • Conclusions

The conclusions of a parametric and a nonparametric test may or may not be different.

The above two properties are different because a nonparametric test and a parametric test involve completely different test statistic computations, although the hypotheses are somewhat the same.

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Most popular questions from this chapter

Finding Critical Values Assume that we have two treatments (A and B) that produce quantitative results, and we have only two observations for treatment A and two observations for treatment B. We cannot use the Wilcoxon signed ranks test given in this section because both sample sizes do not exceed 10.

Rank

Rank Sum of Treatment A

1

2

3

4


A

A

B

B

3

a. Complete the accompanying table by listing the five rows corresponding to the other five possible outcomes, and enter the corresponding rank sums for treatment A.

b. List the possible values of R and their corresponding probabilities. (Assume that the rows of the table from part (a) are equally likely.)

c. Is it possible, at the 0.10 significance level, to reject the null hypothesis that there is no difference between treatments A and B? Explain.

Blanking Out on Tests In a study of students blanking out on tests, the arrangement of test items was studied for its effect on anxiety. The following scores are measures of “debilitating test anxiety” (based on data from “Item Arrangement, Cognitive Entry Characteristics, Sex and Test Anxiety as Predictors of Achievement in Examination Performance,” by Klimko, Journal of Experimental Education, Vol. 52, No. 4.) Is there sufficient evidence to support the claim that the two samples are from populations with different medians? Is there sufficient evidence to support the claim that the arrangement of the test items has an effect on the score? Use a 0.01 significance level.

Questions Arranged From Easy To Difficult

24.64

39.29

16.32

32.83

28.02

33.31

20.6

21.13

26.69

28.9

26.43

24.23

7.1

32.86

21.06

28.89

28.71

31.73

30.02

21.96

25.49

38.81

27.85

30.29

30.72

Questions Arranged From Difficult To Easy

33.62

34.02

26.63

30.26

35.91

26.68

29.49

35.32

27.24

32.34

29.34

33.53

27.62

42.91

30.2

32.54

Radiation in Baby Teeth Listed below are amounts of strontium-90 (in millibecquerels, or mBq, per gram of calcium) in a simple random sample of baby teeth obtained from Pennsylvania residents and New York residents born after 1979 (based on data from “An Unexpected Rise in Strontium-90 in U.S. Deciduous Teeth in the 1990s,” by Mangano et al., Science of the Total Environment). Use a 0.05 significance level to test the claim that the median amount of strontium-90 from Pennsylvania residents is the same as the median from New York residents.

Pennsylvania

155

142

149

130

151

163

151

142

156

133

138

161

New York

133

140

142

131

134

129

128

140

140

140

137

143

Regression If the methods of this section are used with paired sample data, and the conclusion is that there is sufficient evidence to support the claim of a correlation between the two variables, can we use the methods of Section 10-2 to find the regression equation that can be used for predictions? Why or why not?

Using Nonparametric Tests. In Exercises 1–10, use a 0.05 significance level with the indicated test. If no particular test is specified, use the appropriate nonparametric test from this chapter.

Airline Fares Refer to the same data from the preceding exercise. Use the Wilcoxon signed ranks test to test the claim that differences between fares for flights scheduled 1 day in advance and those scheduled 30 days in advance have a median equal to 0. What do the results suggest?
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