Value Stream Management for Lean Healthcare ISE 491

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

Four levels of data l Nominal Ø Ø l Ordinal Ø Ø Ø l 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 Ø Ø Ø l Categorical (Qualitative): Distinct Categories North, South, East, West Bldg. 1, Bldg. 2, Bldg. 7 Continuous (Quantitative): value that can be measured Differences between intervals have true meaning No true zero Scale Ø Ø Continuous (Quantitative): value that can be measured True zero Fall 2009 ISE 491 Dr. Burtner Lecture 7 Slide 2

Parametric Hypothesis Tests l l Assumption of a known distribution, typically the normal distribution Examples Ø Ø Ø 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 2009 ISE 491 Dr. Burtner Lecture 7 Slide 3

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

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

1 -Sample Sign Test l l 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 H 0: median = hypothesized median versus H 1: 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. Fall 2009 ISE 491 Dr. Burtner Lecture 7 Slide 6

1 -Sample Wilcoxon l l 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 H 0: median = hypothesized median versus H 1: 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. Fall 2009 ISE 491 Dr. Burtner Lecture 7 Slide 7

Mann-Whitney Test l l 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 H 0: h 1 = h 2 versus H 1: h 1 ≠ h 2 , 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. Fall 2009 ISE 491 Dr. Burtner Lecture 7 Slide 8

Kruskal-Wallis Test l l l 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: H 0: the population medians are all equal versus H 1: 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. Fall 2009 ISE 491 Dr. Burtner Lecture 7 Slide 9

Friedman test l l Stat > Nonparametrics > 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: H 0: all treatment effects are zero versus H 1: 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. Fall 2009 ISE 491 Dr. Burtner Lecture 7 Slide 10

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