By Daryl S. Paulson
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Extra info for Applied Statistical Designs for the Researcher (Biostatistics)
That is, the sample mean is an unbiased estimate of the population mean. P xi 85 þ 87 þ 92 þ 80 þ 84 428 ¼ ¼ ¼ 85:6 ð1Þ Paint 1 x 1 ¼ n 5 5 P xi 89 þ 89 þ 90 þ 84 þ 88 440 ¼ ¼ ¼ 88:0 ð2Þ Paint 2 x 2 ¼ n 5 5 III. The expression for calculating the Basic Review of Parametric Statistics 27 population variance is: P ðXi À mÞ2 2 ð3Þ s ¼ N where N is the population size, and which is estimated by the sample variance: P ðXi À X Þ2 S2 ¼ ð4Þ nÀ1 Notice that the sample variance formula denominator is n À 1, not n, as one might expect by analogy with the population variance.
II. CALCULATION OF THE ARITHMETIC MEAN AVERAGE The arithmetic mean, or average, is probably the most commonly encountered statistic. Technically, the mean is computed as: n P Xi i¼1 n where Xi ¼ value of the ith observation in the sample n ¼ sample size ¼ total number of values In applied statistics, one can rarely know the population mean value ðmÞ, so it is estimated by the sample mean ðX Þ. The unbiased, expected value of the sample mean is m. That is, the sample mean is an unbiased estimate of the population mean.
The data transformation is usually performed, and the results, call them Yi0 , are reevaluated, generally through another residual analysis. If the residual values (Yi0 À Y^ i0 ) are randomly distributed about zero, the process was adequate. If not, another reexpression iteration can be performed. 4. Resistance, or robustness, of a statistic can be checked using EDA to determine whether a single value, or a few extreme values, has had *In general, reexpressions are ¢rst applied to the response, or dependent variable, y.
Applied Statistical Designs for the Researcher (Biostatistics) by Daryl S. Paulson