Lesson 15 - R

Chapter 15 Review

Objectives

• Summarize the chapter

• Define the vocabulary used

• Complete all objectives

• Successfully answer any of the review exercises

• Use the technology to compute statistical data in the chapter

Nonparametric vs Parametric

• The following nonparametric methods analyze similar problems as parametric methods

The Problem Parametric Nonparametric

Independence of observations

No corresponding procedure

Runs test

Test of central tendency

z-test for the mean

t-test for the mean

Sign test for the median

Test of dependent samples

t-test of the mean of the differences

Wilcoxon signed rank test

Test of independent samples

t-tests of the difference in means

Mann-Whitney test

Correlation Regression Spearman’s rank correlation

Centers of multiple groups

ANOVA (means) Kruskal-Wallis test of distributions

Large vs Small Case Sample Sizes

• The following table breaks down small versus large sample sizes for each nonparametric test

Nonparametric Small Sample Large Sample

Runs Test n1 ≤ 20 and n2 ≤ 20 n1 > 20 or n2 > 20

Sign Test n ≤ 25 n > 25

Wilcoxon Test n ≤ 30 n > 30

Mann-Whitney test n1 ≤ 20 and n2 ≤ 20 n1 > 20 or n2 > 20

Spearman’s Test n ≤ 100 n > 100

Kruskal-WallisTest k = 3 and ni ≤ 5 k > 3 or ni > 5

Problem 1

A difference between parametric statistical methods and nonparametric statistical methods is that

1) Nonparametric statistical methods are better

2) Parametric methods are always easier to compute

3) Nonparametric methods use few, if any, distribution assumptions

4) All of the above

Problem 2

Another name for nonparametric methods is

1) Distribution-free procedures

2) Normal distribution procedures

3) Mean and variance procedures

4) Descriptive methods

Problem 3

The runs test is a test of

1) Whether a set of data has a certain mean

2) Whether a set of data is random

3) Whether a set of data has a certain slope

4) Whether two sets of data have different slopes

Problem 4

In the runs test, if there are very few runs, then we are likely to

1) Reject or do not reject the null hypothesis depending on whether this is a two-tailed, left-tailed, or right-tailed test

2) Reject the null hypothesis that the data are random

3) Not reject the null hypothesis that the data are random

4) All of the above

Problem 5

The sign test is a test of

1) Whether a set of data has a certain mean

2) Whether a set of data is random

3) Whether a set of data has a certain slope

4) Whether a set of data has a certain median

Problem 6

The sign test counts

1) The number of values more than and less than the hypothesized mean

2) The sum of all the positive values of the variable

3) The z-score of the sample median

4) The number of values more than and less than the hypothesized median

Problem 7

The Wilcoxon signed-rank test is a test of

1) Whether two sets of data with matched observations have the same median

2) Whether one set of data has more positive or negative values

3) Whether one set of data has a certain slope

4) Whether two sets of data have the same slopes

Problem 8

To perform the Wilcoxon matched-pairs signed-ranks test, we

1) Compare the number of positive values for the two sets of data

2) Rank the differences of the matched observations

3) Switch the signs of all of the data values

4) All of the above

Problem 9

The Mann-Whitney test is a test of

1) Whether a set of data has a certain mean

2) Whether two sets of data are both random

3) Whether two independent samples have the same medians

4) Whether two independent samples have the same standard deviations

Problem 10

The Mann-Whitney test uses

1) The rankings of each sample’s observations when the two samples are combined

2) A sum of the ranks of one sample’s observations

3) Either a table or an approximation using the normal distribution to find the critical values

4) All of the above

Problem 11

Spearman's rank correlation test is a test of

1) Whether a set of ordered pairs of data has an association

2) Whether a set of ordered pairs of data is listed in a random order

3) Whether two sets of data have the same median

4) Whether two sets of data have the same slope

Problem 12

A group of students enter a contest that has two parts. If the X variable is the student’s rank on the first part and the Y variable is the student’s rank on the second part, then Spearman’s rank correlation test

1) Can be applied because the data is ordered

2) Can be applied because the data is bivariate normal

3) Cannot be applied because ranks cannot be added

4) Cannot be applied because the two variables are dependent

Problem 13

The Kruskal-Wallis test is a test of

1) Whether three or more populations have the same means

2) Whether two variables have a positive association

3) Whether two variables are independent

4) Whether three or more populations have the same distributions

Problem 14

Kruskal-Wallis test differs from ANOVA in that

1) ANOVA is a parametric procedure, Kruskal-Wallis is a nonparametric procedure

2) ANOVA analyzes the difference in means, Kruskal-Wallis analyzes the difference in distributions

3) ANOVA requires the computation of variances, Kruskal-Wallis requires the computation of ranks

4) All of the above

Summary and Homework

• Summary– Nonparametric statistics describes statistical

methods that have few, if any, distribution assumptions

– Nonparametric methods apply in a wide variety of situations, but when both can be used, they are in general not as efficient as parametric methods

– Nonparametric statistical methods often use medians and rankings to perform the analysis

• Homework– problems 1-5 from CD