1. Handbook for Health Care Research, Second Edition Chapter 11 © 2010 Jones and Bartlett Publishers, LLC CHAPTER 11 Statistical Methods for Nominal Measures

2. Handbook for Health Care Research, Second Edition Chapter 11 © 2010 Jones and Bartlett Publishers, LLC Describing the Data Contingency table - used to display counts or frequencies of two or more nominal variables. Proportion- the number of objects of a particular type divided by the total number of objects in the group Percentage- proportion multiplied by 100% Ratio- number of objects in a group with a particular characteristic of interest divided by the number of objects in the same group without the characteristic Odds- A ratio of the probabilities of the two possible states of a binary event. Rate-number of objects occurring per unit of time 2

3. Handbook for Health Care Research, Second Edition Chapter 11 © 2010 Jones and Bartlett Publishers, LLC Characteristics of a Diagnostic Test One of the most common sources of nominal data is diagnostic testing True- and False-Positive Rates (sensitivity)- probability that a test will be positive when the condition of interest is present True- and False-Negative Rates (specificity)- probability that the test will be negative when the condition of interest is absent Sensitivity is the ability of a test to correctly identify patients with the condition of interest 3

4. Handbook for Health Care Research, Second Edition Chapter 11 © 2010 Jones and Bartlett Publishers, LLC Characteristics of a Diagnostic Test Specificity is the ability of a test to correctly identify patients who do not have the condition of interest Positive predictive value of a test is the probability that the condition of interest is present when the test is positive Negative predictive value of a test (or predictive value of a negative test) is the probabil­ity that the condition of interest is absent when the test is negative

5. Handbook for Health Care Research, Second Edition Chapter 11 © 2010 Jones and Bartlett Publishers, LLC Characteristics of a Diagnostic Test Diagnostic Accuracy- proportion of correct results out of all results Likelihood ratio-combines sensitivity and specificity into a single number expressing the odds that the test result occurs in patients with the condition versus those without the condition: likelihood ratio = sensitivity/false positive rate Receiver Operating Characteristic (ROC) Curve- helps compare two diagnostic tests to see which would be most useful 5

6. Handbook for Health Care Research, Second Edition Chapter 11 © 2010 Jones and Bartlett Publishers, LLC ROC 6

7. Handbook for Health Care Research, Second Edition Chapter 11 © 2010 Jones and Bartlett Publishers, LLC Characteristics of a Diagnostic Test Intra­rater reliability index-person measures the same variable twice and the measurements are compared Inter-rater reliability index- two or more people measure the same variable and their measure­ ments are compared Kappa- allows evaluation of the inter-rater reliability: K =observed agreement- � chance agreement 1-chance agreement Phi -is an index of agreement independent of chance: Φ= ad-bc 7

8. Handbook for Health Care Research, Second Edition Chapter 11 © 2010 Jones and Bartlett Publishers, LLC Comparing a Single Sample with a Population Binomial Test- the plotted probability of each outcome from an experiment Z test: z= p-p o 8

9. Handbook for Health Care Research, Second Edition Chapter 11 © 2010 Jones and Bartlett Publishers, LLC Comparing Two Samples, Unmatched Data Unpaired data-data from two independent groups Fisher Exact Test-used for 2 × 2 contingency tables (which have exactly two rows and two columns) – Null Hypothesis: There is no significant difference between the proportion of patients that lived (or died) in ICU A compared with ICU B. 9

10. Handbook for Health Care Research, Second Edition Chapter 11 © 2010 Jones and Bartlett Publishers, LLC Comparing Two or More Samples, Matched Data Paired data-patients act as their own controls McNemar test- is an analysis of contingency tables that have repeated observations of the same individuals. Conditions for use: determining whether or not individuals responded to treatment comparing results of two different treatments on the same people 10

11. Handbook for Health Care Research, Second Edition Chapter 11 © 2010 Jones and Bartlett Publishers, LLC Comparing Three or More Samples, Unmatched Data Chi-squared test- can be used for analyzing contingency tables that are larger than 2 × 2. - Suppose we wanted to test the effectiveness of three different drugs -Null Hypothesis-The proportions are all equal 11