1. Nonparametric Statistical Methods: Overview and Examples
IDM ISE 428
Spring 2011
Dr. Joan Burtner

2. Presented by Dr. Joan Burtner
Four levels of data
Nominal
Categorical (Qualitative): Distinct Categories
North, South, East, West Bldg. 1, Bldg. 2, Bldg. 7
Ordinal
Categorical (Qualitative): Characteristics that possess a logical order
20/20, 20/30, 20/ Small, Medium, Large H,M,L
Special cases
Likert Scales ( ) or ( )
Discrete counted variables (number of calls, number of children, particle counts)
Interval
Continuous (Quantitative): value that can be measured
Differences between intervals have true meaning
No true zero
Scale
True zero
March 2011
Presented by Dr. Joan Burtner

3. Parametric Hypothesis Tests
Assumption of a known distribution, typically the normal distribution
Examples
Single sample T-tests and Z-tests
Two-sample T-tests and Z-tests
Single-factor ANOVA
Two-factor ANOVA
Multi-factor ANOVA
Factorial designs
March 2011
Presented by Dr. Joan Burtner

4. Non-parametric Hypothesis Tests
No assumption of an underlying normal distribution in the population
Other assumptions apply (eg. level of measurement)
Examples (Since names vary by text and software package, you must look at calculation of test statistic and assumptions)
Mann-Whitney
Rank-Sum
Signed Rank
Kruskal-Wallis
Sign
Mood’s Median
Friedman
Median Test
March 2011
Presented by Dr. Joan Burtner

5. Presented by Dr. Joan Burtner
Minitab: Stat Menus
Stat/Non-parametric
Choose from seven non-parametric tests
Names may be different from standard statistics texts
Stat/Multivariate and Stat/DOE
Stat/Tables
One-way and Two-way Chi-Square Tests
Not typically included in discussions of non-parametric statistical methods
Stat/Basic Statistics
Stat/ANOVA
Stat/Regression
March 2011
Presented by Dr. Joan Burtner

6. Minitab: 1-Sample Sign Test
Stat > Nonparametrics > 1-Sample Sign
You can perform a 1-sample sign test of the median or calculate the corresponding point estimate and confidence interval. For the one-sample sign test, the hypotheses are
H0: median = hypothesized median versus H1: median ≠ hypothesized median
Use the sign test as a nonparametric alternative to 1-sample Z-tests and to 1-sample t-tests , which use the mean rather than the median.
March 2011
Presented by Dr. Joan Burtner

7. Minitab: 1-Sample Wilcoxon
Stat > Nonparametrics > 1-Sample Wilcoxon
You can perform a 1-sample Wilcoxon signed rank test of the median or calculate the corresponding point estimate and confidence interval. The Wilcoxon signed rank test hypotheses are
H0: median = hypothesized median versus H1: median ≠ hypothesized median
An assumption for the one-sample Wilcoxon test and confidence interval is that the data are a random sample from a continuous, symmetric population.
March 2011
Presented by Dr. Joan Burtner

8. Minitab: Mann-Whitney Test
Stat > Nonparametrics > Mann-Whitney
You can perform a 2-sample rank test (also called the Mann-Whitney test, or the two-sample Wilcoxon rank sum test) of the equality of two population medians, and calculate the corresponding point estimate and confidence interval. The hypotheses are
H0: h1 = h2 versus H1: h1 ≠ h2 , where h is the population median.
An assumption for the Mann-Whitney test is that the data are independent random samples from two populations that have the same shape and whose variances are equal and a scale that is continuous or ordinal (possesses natural ordering) if discrete.
March 2011
Presented by Dr. Joan Burtner

9. Minitab: Kruskal-Wallis Test
Stat > Nonparametrics > Kruskal-Wallis
You can perform a Kruskal-Wallis test of the equality of medians for two or more populations.
This test is a generalization of the procedure used by the Mann-Whitney test and, like Mood's Median test, offers a nonparametric alternative to the one-way analysis of variance. The Kruskal-Wallis hypotheses are:
H0: the population medians are all equal versus H1: the medians are not all equal
An assumption for this test is that the samples from the different populations are independent random samples from continuous distributions, with the distributions having the same shape.
March 2011
Presented by Dr. Joan Burtner

10. Minitab: Friedman test
Stat > Nonparametrics > Friedman
Friedman test is a nonparametric analysis of a randomized block experiment, and thus provides an alternative to the Two-way analysis of variance. (according to Minitab)
The hypotheses are:
H0: all treatment effects are zero versus
H1: not all treatment effects are zero
Randomized block experiments are a generalization of paired experiments, and the Friedman test is a generalization of the paired sign test. Additivity (fit is sum of treatment and block effect) is not required for the test, but is required for the estimate of the treatment effects.
March 2011
Presented by Dr. Joan Burtner

11. Examples from Statistics Texts
Rosner (Biomedical)
Daniel (Biomedical)
Walpole, Myers, Myers, and Ye (Engineering)
Montgomery (Engineering)
Montgomery and Runger (Engineering)
Campbell, M. , Machin, D, and Walters, S. (Medical)
Berenson and Levin (Business)
March 2011
Presented by Dr. Joan Burtner

12. Observations from Statistics Guides
Minitab Help
Minitab Statistics Guide
SPSS Help
Field, Andy (SPSS)
Green, Salkind, and Akey (SPSS)
Norman and Streiner (Comprehensive statistics text with a strong emphasis on explanations)
March 2011
Presented by Dr. Joan Burtner