ABSTRACT
Shaping sample data with descriptive tools is only the first step in statistical analysis. Several useful and interesting tasks can be performed with other techniques in the statistical toolbox. The most common of these tasks is undoubtedly the comparison of data from different samples to assess the likelihood that the subjects in the samples come from different populations. The tool to study differences is inferential statistics. Literally, its name reflects the need to make inferences-to arrive at a conclusion by reasoning from incomplete evidence, according to Webster’s-since we do not know everything about the situation. (This sounds like the daily circumstance of today’s health professionals, yes?)
The proper application and the meaningful interpretation of inferential statistics both require understanding the tool’s theoretical basis. Researchers who do not know the underlying theory can create misleading information, and decision makers who do not understand the theory can be misled. I have concluded after a quarter century of teaching that the essential theoretical foundations of inferential statistics are not adequately presented in most statistics texts or courses. Therefore, consistent with my goal of emphasizing understanding over believing, this chapter puts the emphasis on theory in order to correct the imbalance that leads to bad decisions. (My students are almost all very smart, so I feel comfortable placing the blame on the instructional side. If the theory behind inferential statistics had been well presented, they would have learned it.)
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Inferential statistics is made possible by the characteristics of a very special distribution, the famous “bell-shaped” curve.1 It is also called the normal or Gaussian distribution (after a nineteenth-century German mathematician, Carl Gauss, who elaborated the properties of a distribution originally developed during the seventeenth century by a Swiss theologian named Jacques Bernoulli).2 It is illustrated in Figure 6.1.
