1. Value Stream Management for Lean Healthcare ISE 491 Fall 2009 Data Analysis - Lecture 7

2. Fall 2009ISE 491 Dr. Burtner Lecture 7 Slide 2 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, 20/40 Small, Medium, Large H,M,L  Special case 1 2 3 4 5 (Likert Scale) Interval  Continuous (Quantitative): value that can be measured  Differences between intervals have true meaning  No true zero Scale  Continuous (Quantitative): value that can be measured  True zero Fall 2009ISE 491 Dr. Burtner

3. Fall 2009ISE 491 Dr. Burtner Lecture 7 Slide 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 Fall 2009ISE 491 Dr. Burtner

4. Fall 2009ISE 491 Dr. Burtner Lecture 7 Slide 4 Non-parametric Hypothesis Tests No assumption of an underlying normal distribution in the population Other assumptions may apply Examples  Mann-Whitney  Rank-Sum  Kruskal-Wallis  Sign  Moody’s Median Fall 2009ISE 491 Dr. Burtner

5. Fall 2009ISE 491 Dr. Burtner Lecture 7 Slide 5 Hypothesis Testing in Minitab Stat/Non-parametric  Choose from seven non-parametric tests  Names may be different from Walpole and Myers text Stat/Multivariate and Stat/DOE  Beyond the scope of this course Stat/Tables  One-way and Two-way Chi-Square Tests Stat/Basic Statistics Stat/ANOVA Stat/Regression Fall 2009ISE 491 Dr. Burtner

6. Fall 2009ISE 491 Dr. Burtner Lecture 7 Slide 6 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.1- sample Z-tests1-sample t-tests

7. Fall 2009ISE 491 Dr. Burtner Lecture 7 Slide 7 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.

8. Fall 2009ISE 491 Dr. Burtner Lecture 7 Slide 8 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.

9. Fall 2009ISE 491 Dr. Burtner Lecture 7 Slide 9 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:Mann- Whitney 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.

10. Fall 2009ISE 491 Dr. Burtner Lecture 7 Slide 10 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. The hypotheses are:Two-way 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.

11. Fall 2009ISE 491 Dr. Burtner Lecture 7 Slide 11 Primary Source Minitab Help Guide