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the t value required

Therefore, the standard error of the mean for biologic dura-tion is computed as follows: sX=12210. sX=039. The standard error of the mean for biologic duration is 0.39. Confi dence Intervals To determine how closely the sample mean approximates the population mean, the stan-dard error of the mean is used to build a confi dence interval. For that matter, a confi dence interval can be created for many statistics, such as a mean, proportion, and odds ratio. To build a confi dence interval around a statistic, you must have the standard error value and the t value to adjust the standard error. The degrees of freedom ( df ) to use to compute a confi dence interval is df = n − 1. To compute the confi dence interval for a mean, the lower and upper limits of that interval are created by multiplying the sX by the t statistic, where df = n − 1. For a 95% confi dence interval, the t value should be selected at α = 0.05. For a 99% confi dence inter-val, the t value should be selected at α = 0.01. Using the biologic medication duration data, we know that the standard error of the mean duration of biologic medication use is sX=039. . The mean duration of biologic medication use is 1.89. Therefore, the 95% confi dence interval for the mean duration of biologic medication use is computed as follows: XstX± 189039226…±()() 189088..± As referenced in Appendix A , the t value required for the 95% confi dence interval with df = 9 is 2.26. The computation above results in a lower limit of 1.01 and an upper limit of 2.77. This means that our confi dence interval of 1.01 to 2.77 estimates the population mean duration of biologic use with 95% confi dence ( Kline, 2004 ). Technically and math-ematically, it means that if we computed the mean duration of biologic medication use on an infi nite number of veterans, exactly 95% of the intervals would contain the true population mean, and 5% would not contain the population mean ( Gliner, Morgan, & Leech, 2009 ). If we were to compute a 99% confi dence interval, we would require the t value that is referenced at α = 0.01. Therefore, the 99% confi dence interval for the mean duration of biologic medication use is computed as follows: 189039325…±()() 189127..± 297Calculating Descriptive Statistics • EXERCISE 27Copyright © 2017, Elsevier Inc. All rights reserved. As referenced in Appendix A , the t value required for the 99% confi dence interval with df = 9 is 3.25. The computation above results in a lower limit of 0.62 and an upper limit of 3.16. This means that our confi dence interval of 0.62 to 3.16 estimates the population mean duration of biologic use with 99% confi dence. Degrees of Freedom The concept of degrees of freedom ( df ) was used in reference to computing a confi dence interval. For any statistical computation, degrees of freedom are the number of inde-pendent pieces of information that are free to vary in order to estimate another piece of information ( Zar, 2010 ). In the case of the confi dence interval, the degrees of freedom are n − 1. This means that there are n − 1 independent observations in the sample that are free to vary (to be any value) to estimate the lower and upper limits of the confi dence interval.

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