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MEASURES OF DISPERSION

The formula for calculating the mean is as follows: XXn=∑ where X = mean ∑ = sigma, the statistical symbol for summation X = a single value in the sample n = total number of values in the sample The mean number of years that the veterans used a biologic medication is calculated as follows: X=+++++++++()=010313151520223030401019………..years TABLE 27-1 DURATION OF BIOLOGIC USE AMONG VETERANS WITH RHEUMATOID ARTHRITIS ( n = 10) Duration of Biologic Use (years) 0.10.31.31.51.52.02.23.03.04.0 293Calculating Descriptive Statistics • EXERCISE 27Copyright © 2017, Elsevier Inc. All rights reserved. The mean is an appropriate measure of central tendency for approximately normally distributed populations with variables measured at the interval or ratio level. It is also appropriate for ordinal level data such as Likert scale values, where higher numbers rep-resent more of the construct being measured and lower numbers represent less of the construct (such as pain levels, patient satisfaction, depression, and health status). The mean is sensitive to extreme scores such as outliers. An outlier is a value in a sample data set that is unusually low or unusually high in the context of the rest of the sample data. An example of an outlier in the data presented in Table 27-1 might be a value such as 11. The existing values range from 0.1 to 4.0, meaning that no veteran used a biologic beyond 4 years. If an additional veteran were added to the sample and that person used a biologic for 11 years, the mean would be much larger: 2.7 years. Simply adding this outlier to the sample nearly doubled the mean value. The outlier would also change the frequency distribution. Without the outlier, the frequency distribution is approximately normal, as shown in Figure 27-1 . Including the outlier changes the shape of the distribution to appear positively skewed. Although the use of summary statistics has been the traditional approach to describing data or describing the characteristics of the sample before inferential statistical analysis, its ability to clarify the nature of data is limited. For example, using measures of central tendency, particularly the mean, to describe the nature of the data obscures the impact of extreme values or deviations in the data. Thus, signifi cant features in the data may be concealed or misrepresented. Often, anomalous, unexpected, or problematic data and discrepant patterns are evident, but are not regarded as meaningful. Measures of disper-sion, such as the range, difference scores, variance, and standard deviation ( SD ), provide important insight into the nature of the data. MEASURES OF DISPERSION Measures of dispersion , or variability, are measures of individual differences of the members of the population and sample.

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