Southwest Technology Consultants

  Excellence In:
Statistical Consulting
Statistical Training
Data Analysis
Applied Nonparametric Statistics
Introduction

Statistical methods for the analysis of data are generally classified as being either parametric or nonparametric. Parametric procedures are characterized by assumptions, such as normality, whose validity is frequently questionable in many applications. On the other hand, nonparametric procedures employ simpler models, yet these models can be more robust and powerful than their parametric counterparts.

If a wrong decision is costly, statistical methods should not be based on assumptions that appear to be invalid. Hence, nonparametric methods are essential tools for statistical analyses. There are numerous nonparametric procedures and the following list shows only some well known parametric procedures followed by a list of their corresponding nonparametric counterparts.

Parametric Procedure

  • Paired t-test

  • Two-sample t-test

  • Pearsonís correlation

  • Completely randomized design (one-way AOV)

  • Randomized complete block

Nonparametric Procedure

  • Wilcoxon signed-rank test

  • Wilcoxon-Mann-Whitney rank sum test

  • Spearmanís rho

  • Kruskal-Wallis test

  • Friedmanís test

These nonparametric procedures and many others form the basis for this short course.

What You Will Learn

Course participants will gain an understanding of the value of checking test assumptions and applying the appropriate nonparametric procedure when these assumptions are questionable. In particular, attendees will learn how to:

  • Check for test assumptions
  • Apply nonparametric procedures
  • Compare parametric and nonparametric test results
  • Calculate robustness and power
  • Interpret test results
  • Communicate results to decision makers
Course Content

The following topics will be covered:

  • Overview of nonparametric and parametric statistics
  • Displaying data as an empirical distribution function (needed for many nonparametric procedures)
  • Lilliefors (graphical) test for normality
  • Distribution of the sample mean when the population is not normal, in particular, this refers to the use of ranks in nonparametric tests and also provides strong rational for the use of control charts to monitor the mean in SPC
  • Binomial test - comparing the success rate of a new process against a known value or standard including sample size requirements for a given level of significance and a desired power
  • Confidence interval for the median (optional depending on participant needs)
  • Median test
  • Wilcoxon signed-ranks test for paired data including the null distribution for small sample sizes, the effect of ties in the ranks and large sample approximation based on the familiar paired t-test.
  • Wilcoxon-Mann-Whitney rank sum test for two independent samples including the null distribution for small sample sizes, the effect of ties in the ranks and large sample approximation based on the familiar two-sample t-test.
  • Contingency tables (optional depending on time and participant  needs)
  • Goodness-of-fit test (optional depending on time and participant  needs)
  • Spearmanís rank correlation including the null distribution for small sample sizes, the effect of ties in the ranks and large sample approximation based on Pearsonís product correlation coefficient.
  • Monotone regression (regression using ranks)ódemonstrated for simple linear regression, but easily extendable to multiple linear regression (optional depending on time and participant needs)
  • Kruskal-Wallis test for one-factor experimentsóincludes the null distribution for small sample sizes, the effect of ties in the ranks, and large sample approximation based on the familiar F-test from a one-factor AOV.
  • Friedman test for blocked experiments using process equipment performance including the null distribution for small sample sizes, the effect of ties in the ranks, and large sample approximation based on the familiar F-test from a two-factor AOV.
  • Analysis of covariance (optional depending on time and participant  needs)
  • Rank transformations and interaction
 

 


Contact Information

Phone: 505 856-6500

Email: stc@swtechcon.com

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