Download presentation

1
**Introduction to Nonparametric Statistics**

CD-ROM Chapter 15 Introduction to Nonparametric Statistics

2
**Chapter 15 - Chapter Outcomes**

After studying the material in this chapter, you should be able to: Recognize when and how to use the runs test and testing for randomness. Know when and how to perform a Mann-Whitney U test. Recognize the situations for which the Wilcoxon signed rank test applies and be able to use it in a decision-making context. Perform nonparametric analysis of variance using the Kruskal-Wallis one-way ANOVA.

3
**Nonparametric Statistics**

Nonparametric statistical procedures are those statistical methods that do not concern themselves with population distributions and/or parameters.

4
The Runs Test The runs test is a statistical procedure used to determine whether the pattern of occurrences of two types of observations is determined by a random process.

5
The Runs Test A run is a succession of occurrences of a certain type preceded and followed by occurrences of the alternate type or by no occurrences at all.

6
The Runs Test (Table 15-1)

7
**The Runs Test (Small Sample Example)**

H0: Computer-generated numbers are random between 0.0 and 1.0. HA: Computer-generated numbers are not random . Runs: There are r = 10 runs From runs table (Appendix K) with n1 = 9 and n2 = 11, the critical value of r is 6

8
**The Runs Test (Small Sample Example)**

Test Statistic: r = 10 runs Critical Values from Runs Table: Possible Runs: Reject H0 Reject H0 Do not reject H0 Decision: Since r = 10, we do not reject the null hypothesis.

9
**MEAN AND STANDARD DEVIATION FOR r**

Large Sample Runs Test MEAN AND STANDARD DEVIATION FOR r where: n1 = Number of occurrences of first type n2 = Number of occurrences of second type

10
**TEST STATISTIC FOR LARGE SAMPLE RUNS TEST**

11
**Large Sample Runs Test (Example 15-2)**

Table 15-2 OOOUOOUOUUOOUUOOOOUUOUUOOO UUUOOOOUUOOUUUOUUOOUUUUU OOOUOUUOOOUOOOOUUUOUUOOOU OOUUOUOOUUUOUUOOOOUUUOOO n1 = 53 “O’s” n2 = 47 “U’s” r = 45 runs

12
**Large Sample Runs Test (Example 15-2)**

H0: Yogurt fill amounts are randomly distributed above and below 24-ounce level. H1: Yogurt fill amounts are not randomly distributed above and below 24-ounce level. = 0.05 Rejection Region /2 = 0.025 Rejection Region /2 = 0.025 Since z= > and < 1.96, we do not reject H0,

13
**Mann-Whitney U Test • The two samples are independent and random.**

The Mann Whitney U test can be used to compare two samples from two populations if the following assumptions are satisfied: • The two samples are independent and random. • The value measured is a continuous variable. • The measurement scale used is at least ordinal. • If they differ, the distributions of the two populations will differ only with respect to the central location.

14
**Mann-Whitney U Test U-STATISTICS where:**

n1 and n2 are the two sample sizes R1 and R2 = Sum of ranks for samples 1 and 2

15
**Mann-Whitney U Test - Large Samples -**

MEAN AND STANDARD DEVIATION FOR THE U-STATISTIC where: n1 and n2 = Sample sizes from populations 1 and 2

16
**Mann-Whitney U Test - Large Samples -**

MANN-WHITNEY U-TEST STATISTIC

17
**Mann-Whitney U Test (Example 15-4)**

Rejection Region = 0.05 Since z= > , we do not reject H0,

18
**Wilcoxon Matched-Pairs Test**

The Wilcoxon matched pairs signed rank test can be used in those cases where the following assumptions are satisfied: • The differences are measured on a continuous variable. • The measurement scale used is at least interval. • The distribution of the population differences is symmetric about their median.

19
**Wilcoxon Matched-Pairs Test**

WILCOXON MEAN AND STANDARD DEVIATION where: n = Number of paired values

20
**Wilcoxon Matched-Pairs Test**

WILCOXON TEST STATISTIC

21
**Kruskal-Wallis One-Way Analysis of Variance**

Kruskal-Wallis one-way analysis of variance can be used in one-way analysis of variance if the variables satisfy the following: • They have a continuous distribution. • The data are at least ordinal. • The samples are independent. • The samples come from populations whose only possible difference is that at least one may have a different central location than the others.

22
**Kruskal-Wallis One-Way Analysis of Variance**

H-STATISTIC where: N = Sum of sample sizes in all samples k = Number of samples Ri = Sum of ranks in the ith sample ni = Size of the ith sample

23
**Kruskal-Wallis One-Way Analysis of Variance**

CORRECTION FOR TIED RANKINGS where: g = Number of different groups of ties ti = Number of tied observations in the ith tied group of scores N = Total number of observations

24
**Kruskal-Wallis One-Way Analysis of Variance**

H-STATISTIC CORRECTED FOR TIED RANKINGS

25
**Key Terms • Kruskal-Wallis One-Way Analysis of Variance • Run**

• Mann-Whitney U Test • Nonparametric Statistical Procedure • Run • Runs Test • Wilcoxon Test

Similar presentations

OK

Wilcoxon Tests What is the Purpose of Wilcoxon Tests? What are the Assumptions? How does the Wilcoxon Rank-Sum Test Work? How does the Wilcoxon Matched-

Wilcoxon Tests What is the Purpose of Wilcoxon Tests? What are the Assumptions? How does the Wilcoxon Rank-Sum Test Work? How does the Wilcoxon Matched-

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Download ppt on pollution Ppt on op amp circuits offset Extraocular muscles anatomy and physiology ppt on cells Ppt on 3-phase squirrel cage induction motor Ppt on cloud technology Ppt on satellite orbital locations Ppt on forest fire in india Ppt on power sharing in indian and other countries Ppt on sectors of economy for class 10 Ppt on indian festivals in hindi