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biologic medication duration data

The formula for the mean deviation is: XXXndeviation=−∑ In this example, the mean deviation is 0.95. This value was calculated by taking the sum of the absolute value of each difference score (1.8, 1.6, 0.6, 0.4, 0.4, 0.1, 0.3, 1.1, 1.1, 2.1) and dividing by 10. The result indicates that, on average, subjects ’ duration of biologic use deviated from the mean by 0.95 years. Variance Variance is another measure commonly used in statistical analysis. The equation for a sample variance ( s 2 ) is below. sXXn221=−()−∑ 295Calculating Descriptive Statistics • EXERCISE 27Copyright © 2017, Elsevier Inc. All rights reserved. Note that the lowercase letter s 2 is used to represent a sample variance. The lowercase Greek sigma ( σ 2 ) is used to represent a population variance, in which the denominator is N instead of n − 1. Because most nursing research is conducted using samples, not popu-lations, formulas in the subsequent exercises that contain a variance or standard deviation will incorporate the sample notation, using n − 1 as the denominator. Moreover, statistical software packages compute the variance and standard deviation using the sample formu-las, not the population formulas. The variance is always a positive value and has no upper limit. In general, the larger the variance, the larger the dispersion of scores. The variance is most often computed to derive the standard deviation because, unlike the variance, the standard deviation refl ects impor-tant properties about the frequency distribution of the variable it represents. Table 27-3 displays how we would compute a variance by hand, using the biologic duration data. s213419=. s²=1.49 TABLE 27-3 VARIANCE COMPUTATION OF BIOLOGIC USE X X XX– XX–(())2 0.1 − 1.9 − − 1.9 − 1.62.561.3 − 1.9 − 0.60.361.5 − 1.9 − − 1.9 − − − − − − Σ 13.41 Standard Deviation Standard deviation is a measure of dispersion that is the square root of the variance. The standard deviation is represented by the notation s or SD . The equation for obtaining a standard deviation is SDX=−()−∑Xn21 Table 27-3 displays the computations for the variance. To compute the SD , simply take the square root of the variance. We know that the variance of biologic duration is s 2 = 1.49. Therefore, the s of biologic duration is SD = 1.22. The SD is an important sta-tistic, both for understanding dispersion within a distribution and for interpreting the relationship of a particular value to the distribution. SAMPLING ERROR A standard error describes the extent of sampling error. For example, a standard error of the mean is calculated to determine the magnitude of the variability associated with the mean. A small standard error is an indication that the sample mean is close to 296EXERCISE 27 • Calculating Descriptive StatisticsCopyright © 2017, Elsevier Inc. All rights reserved. the population mean, while a large standard error yields less certainty that the sample mean approximates the population mean. The formula for the standard error of the mean ( sX ) is: ssnX= Using the biologic medication duration data, we know that the standard deviation of biologic duration is s = 1.22.

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