Many of the concepts and technologies of biomedical optics, as introduced in this text, are intended as novel, and often minimally invasive, diagnostic methods that are capable of measuring or sensing a variety of physiological parameters. To facilitate understanding the value of novel diagnostics, we introduce here some of the statistical concepts that are most commonly used to assess the reliability of a diagnostic test. As such, we are limiting discussion to a narrow range of the statistical issues in medicine. Among a substantial number of other classes of statistical analysis are: verification that one treatment is superior to another (or to placebo); determining dosage equivalence of two treatments; estimating the mean value of a physiological parameter in a population; measuring the prevalence of a disease in a sample population (for example, to determine whether the disease prevalence is growing); estimating the prevalence of a condition in the general population based on measurements in a sample of the population. All of these require determinations of statistical significance, often invoking measures such as paired and unpaired “t-tests” and “p-values,” and each type of assessment has different criteria, but those considerations are outside the scope of this chapter.

When developing a new diagnostic method or medical test it is always necessary to determine how well the method works by statistical methods. Why? Let us pose a very simple, non-medical problem (and not related to diagnosis). Imagine you have a friend who lives in a small town that recently installed its first traffic light at a central intersection, which was previously controlled by four-way stop signs. After two years the mayor announces that the accident rate at that intersection was lower in 2013 than it had been in 2012. Consequently, the mayor's office is asking the Town Council to raise taxes so that they can install five more traffic lights at other intersections. At a Town Council meeting a concerned citizen asks for the numbers: how many accidents have there been in those two years? The mayor, who wants to take credit for the improvement, is quick to respond that there were 42 accidents in 2012 and “only” 37 in 2013, a 12% drop. He claims that this is “significant” and that he expects the improvement to continue. Economic times are tough, however, so installation of more lights is delayed a couple of years.