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What Are We Summarizing? Lecture 11 Sections 4.1 – 4.2 Tue, Feb 1, 2005 What Are We Summarizing? There are various types of data. How the data are summarized depends on the type of data. See Data Set 1, p. 184. How best to summarize Gender? How best to summarize Age? How best to summarize Blood Pressure? Qualitative Variables Qualitative variable – A variable whose values are not numerical, but can be divided into categories. The values of a qualitative variable may or may not have a natural order. Examples: Gender. Questionnaire response, from strongly agree to strongly disagree. Quantitative Variables Quantitative variable – A variable whose values are numerical. A quantitative variable may be continuous or discrete. Continuous Variables Continuous variable – The set of theoretically possible values of the variable forms a continuous set of real numbers. Typically these are measured quantities: length, time, area, weight, etc. Example: The length of time a student takes to complete a test. Usually modified by “much,” not “many.” How much time will it take? Discrete Variables Discrete variable – The set of theoretically possible values of the variable forms a set of isolated points on the number line. Typically this is count data; a verbal description usually contains the phrase “the number of.” Example: The number of students who completed the test within 40 minutes. Usually modified by “many,” not “much.” How many students finishes the test? Discrete vs. Continuous Some data may be considered to be either discrete or continuous. Example: Time. How much time do I have for the test? How many minutes do I have for the test? Example: Money. How much money is in your pocket? How many dollars are in your pocket? In such cases, consider it to be continuous. Discrete vs. Continuous Some data may be considered to be either discrete or continuous. Example: Time. How much time do I have for the test? How many minutes do I have for the test? Example: Money. How much money is in your pocket? How many dollars are in your pocket? In such cases, consider it to be continuous. Discrete vs. Continuous The distinction is based on the nature of the variable, not the manner in which it is measured or recorded. Example: Measure the time it takes each student to finish a test, to the nearest minute. The possible times are 0, 1, 2, 3, … minutes. Is that discrete or continuous? Let’s Do It! Think about it, p. 188. Let’s do it! 4.1, p. 187 – What Type of Variable? Example Revisit the study one more time. The Role of Cyclooxygenase-2 Inhibitors in Fusion Rates of Hindfoot Arthrodesis What kind of data were collected? How were these data summarized? COX-2 Study The group that received the COX-2 inhibitor medication had an overall nonunion rate of 11.2%. For all patients that achieved arthrodesis, average time to union was 89.8 days for this group. When separated by arthrodesis site, the majority of nonunions were failed ankle arthrodesis (96%). COX-2 Study In the group that did not receive a COX-2 inhibitor postoperatively, the overall nonunion rate was 12.4%, again with failed ankle arthrodesis accounting for the majority of the nonunions (97%). Time to union in this group averaged 93.4 days. COX-2 Study The time to union was shorter in the group that received COX-2 inhibitors, but this was not statistically significant. The overall nonunion rate was lower in the group that received COX-2 inhibitors, but this, too, was not statistically significant.