Leonard -- Math 391 Topics in Nonparametric Statistics -- Spring 2019 -- SDSMT

Course Information

• Course Syllabus

Homework Assignments

• Homework #1: Find two data sets: one which appears to be drawn from a normal population, and one which appears to be drawn from a population which is not normal. Defend your conclusions using Q-Q plots and the Shapiro-Wilk test. This assignment will be worth two points. Please submit your results to me by 12PM on Tuesday, January 22.

• Homework #2: Here's the assignment. We'll discuss a due date in class.

Other Resources

• Week One: A Quick Rundown of Useful Distributions

  • Handout

  • Geogebra File for t-distributions

  • Geogebra File for chi-squared distributions

  • Geogebra File for F-distributions

• Week Two: Assessing Normality

  • Handout

  • A paper by Shapiro & Wilk about the aptly-named Shapiro-Wilk test for normality.

  • A paper by Seier comparing the statistical power of several normality tests.

  • A paper by Razali & Wah comparing statistical power of four normality tests.

  • A paper by Ahmad & Sherwani comparing statistical power of twelve normality tests.

  • A link to some information about an "expanded" Shapiro-Wilk test. I haven't verified the results, use at your own peril.

• Week Three: The Wilcoxon Signed-Rank Test for One Population Median

  • Handout

  • A link to a handout by Charles Geyer (faculty at UMN Minneapolis) which, among other things, discusses how to generate a confidence interval for a (pseudo)median using Walsh averages. See section 2.3 of his handout.

    • In R, add the options conf.int=TRUE and conf.level=c to a two-sided wilcox.test command to generate such an interval for the pseudomedian. Your confidence level should be in decimal form, and (as Geyer warns) the returned interval will usually not have precisely the level of confidence you specify (but, hopefully, something close).

  • A link to Wilcoxon's original paper in 1945.

  • A link to a paper by Paolo Toccaceli which studies the power of WSRT using Wilcoxon's and Pratt's methods for dealing with zero ranks.

    • Mr. Toccaceli appears to work for the Computer Learning Research Centre at Royal Holloway University of London.

    • Consequently, despite the informal nature of this article, I presume that Toccaceli had some informal peer review.

    • Nonetheless, use the given information with caution. Of note: Toccaceli concludes that while both approaches to zero ranks tend to be conservative, Pratt's method was much more so.

  • A link to a paper by Imam, Usman, and Chiawa which compares the power of the t-test, Sign Test, and WSRT.

  • An online article which discusses exact implementations for both Wilcoxon's and Pratt's approach to zero ranks.

  • If you would like to review the traditional t-tests (hypothesis tests and confidence intervals) for one population mean which assume normalishness of the underlying population, feel free to review the following documents (the section numbers correspond to the Navidi text currently used in SDSMT MATH/IENG 381 courses):

    • Sections 6.1/6.2/6.4: Hypothesis Testing for One Mean

      • Summary and Suggested Practice Problems

      • Solutions to Additional Practice Problems

    • Sections 5.1/5.3.2: Confidence Intervals for One Mean

      • Summary and Suggested Practice Problems

      • Solutions to Additional Practice Problems

• Week Four: Chi-Squared Tests (Single Variance Testing & Pearson's Goodness of Fit)

  • Handout

• Week Five: Tests for Several Variances (Bartlett's Test & the Brown/Forsythe/Levene Test)

  • Handout (UPDATED: February 5 to fix a typo in the w-statistic for the Brown/Forsythe/Levene Test

• Week Six: The t-Tests for Two Independent Population Means

  • Handout

  • An article discussing the formula for degrees of freedom in the unequal variance case (by Michael Allwood).

• Week Seven: The Location/Scale Tests of Lepage and Cucconi

  • Handout

  • A paper by Marozzi discussing the Lepage and Cucconi tests.

  • Documentation for the tpepler/nonpar package.

  • Documentation for the Lepage test in tpepler/nonpar.

  • Documentation for the Cucconi test in tpepler/nonpar.

• Week Eight: The Wilcoxon-Mann-Whitney Rank Sum Test for Two Independent Populations

  • Handout

• Week Nine: Paired Data & The Wilcoxon Signed-Rank Test

  • Handout

• Week Eleven: Some Multiple Comparison Methods for Independent Populations

  • Handout

• Week Thirteen: Repeated Measures ANOVA & The Quade Test

  • Handout

  • A link to an article discussing the Greenhouse-Geisser and Huynh-Feldt Corrections

  • A link to a discussion of the use of ezANOVA in R

  • A link to the documentation for the Quade Test in R