Applied Statistical Designs for the Researcher by Daryl S. Paulson

By Daryl S. Paulson

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The median is the central value in an ordered array of values. y If y is a ‘‘normal’’ random variable, then the probability distribution function of y is 1 1 ðY ÀmÞ 2 f ðY Þ ¼ pffiffiffiffiffiffi eð2Þð s Þ s 2p where À1 < m < 1 is the mean of the distribution and s2 > 0 is the variance. Basic Review of Parametric Statistics 23 FIGURE 2 Nonnormal distributions. measured in standard deviations, that separates the end points a and b from the mean. For example, about 68% of the values in a normal population lie within one standard deviation (plus and minus) from the mean, from m À s to m þ s.

They straggle more than they should according to statistical theory [14]. Yet, these straggler valuesösometimes single, sometimes multipleöcan reveal valuable hidden features contained in the data. For example, the antimicrobial e⁄cacy (log10 microbial count) data in human trials of a preoperative skin prepping solution often have straggler values (also known as ‘‘outliers’’) that are either very large or very small, relative to the data’s central tendency. Generally, upon investigation, this is not an anomaly related to the degerming characteristics of the antimicrobial solution but is a phenomenon both of bacterial populations normally residing on the skin surfaces and of skin sampling methods themselves.

Finally, it is important to recognize that use of these four EDA tools together will maximize their e⁄ciency. ,very di¡erent from the other data in the set), a data display, such as the stem-and-leaf display, will portray them quickly. A residual analysis will also portray this situation, not in terms of the actual numbers but in di¡erences (ei ) between the observed and predicted values. And, if the data are skewedöpiled to the left (smaller values) or piled to the right (larger values) with a long tail on the opposite endö reexpressing the data, in most cases, will be useful in making the data more normal in their distribution.

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