1. Handbook for Health Care Research, Second Edition Chapter 12 © 2010 Jones and Bartlett Publishers, LLC CHAPTER 12 Statistical Methods for Ordinal Measures

2. Handbook for Health Care Research, Second Edition Chapter 12 © 2010 Jones and Bartlett Publishers, LLC Describing the Data Contingency- used to display counts or frequencies of two or more ordinal variables Calculation of a mean is not appropriate for ordinal data Ordinal data are commonly presented with bar graphs or pie charts 2

3. Handbook for Health Care Research, Second Edition Chapter 12 © 2010 Jones and Bartlett Publishers, LLC Correlation Spearman Rank Order Correlation(also called Spearman’s rho or rank correlation) - is a nonparametric test that does not require the data points to be linearly related -rho has a value between -1 to +1 Appropriate to use : - to measure the strength of association between pairs of ordinal variables or between an ordinal variable and a continuous variable. - to reduce the effect of extreme values on the correlation of data on the continuous level of measurement 3

4. Handbook for Health Care Research, Second Edition Chapter 12 © 2010 Jones and Bartlett Publishers, LLC Spearman Rank Order Correlation Example You suspect that Apgar scores are correlated with infants’ birth weight. You collect the data in below on a group of newborns. Null Hypothesis: Weight (when converted to an ordinal scale) is not associated with Apgar score. 4

5. Handbook for Health Care Research, Second Edition Chapter 12 © 2010 Jones and Bartlett Publishers, LLC Comparing Two Samples, Unmatched Data Mann-Whitney Rank Sum Test ( also known as Whitney U test or the Wilcoxon rank sum test) -tests the hypothesis that the medians of two different samples are the same -Non­parametric alternative to the unpaired t test 5

6. Handbook for Health Care Research, Second Edition Chapter 12 © 2010 Jones and Bartlett Publishers, LLC Mann-Whitney Rank Sum Test Example: You want to test the performance of a new supervisor (A) by comparing her assessment skills with those of a more experienced supervisor (B). Each supervisor assesses the same eight patients on a scale of 1 to 5 Null Hypothesis - There is no difference between these groups of triage scores; the two sets of data were not drawn from populations with different medians. p= 0.442 not statistically significant difference 6

7. Handbook for Health Care Research, Second Edition Chapter 12 © 2010 Jones and Bartlett Publishers, LLC Comparing Two Samples, Matched Data Kruskal-Wallis ANOVA-tests the hypothesis that the groups are the same versus the hypothesis that at least one of the groups is different from the others. -Nonparametric alternative to the one-way (or one factor) analysis of variance 7

8. Handbook for Health Care Research, Second Edition Chapter 12 © 2010 Jones and Bartlett Publishers, LLC Wilcoxon Signed Rank Test Example- Your department has just completed a training program for therapists who will participate in a respiratory therapy consult service. The consult service employs standardized assessment procedures to assign triage scores to patients according to their disease type and severity. To test the effectiveness of the training program, you select a new therapist and ask him to assign triage scores (1 through 5) to a set of seven simulated patients before and after training Null- There is no difference in the two groups of data. 8

9. Handbook for Health Care Research, Second Edition Chapter 12 © 2010 Jones and Bartlett Publishers, LLC Comparing Three or More Samples, Matched Data Friedman Repeated Measures ANOVA- examines if a single group of individuals was affected by a series of three or more different experimental treatments, in which each individual received all treatments – Nonparametric alternative to a one-way repeated measures analysis of variance 9

10. Handbook for Health Care Research, Second Edition Chapter 12 © 2010 Jones and Bartlett Publishers, LLC Kruskal-Wallis ANOVA Example- Your department has been trying to decide on the appropriate length of a training program for therapists who will participate in a respiratory therapy consult service. The consult service employs standardized assessment procedures to assign triage scores to patients according to disease type and severity. To test the effectiveness of different training program lengths, you select three groups of seven new therapists and grade their assessment skills (grade 0 through 5) on simulated patients after each of three training sessions Null Hypothesis -All three sets of data came from the same population; there are no differences among the groups 10