Bayesian Statistics for Biological Data: Pedigree Analysis
William D. Stansfield, Matthew A. Carlton · The American Biology Teacher · 2004
I n teaching biology, there may be a tendency to concentrate too much on the descriptive aspects of the subject.A well-rounded education in the biological sciences also requires experience in the gathering and statistical analysis (interpretation) of quantitative data from field or laboratory studies.There are numerous mathematical tools and computer programs to help us do this today.Introducing students to some of these tools and their practical applications should be part of every biology class.One of these tools is known as Bayesian analysis.The specific purposes of this report are to: * Introduce Bayes' formula.* Demonstrate its application to the biological problem of pedigree analysis.* Illustrate that Bayes' formula and non-Bayesian or "classical" methods of probability calculation may yield different answers.It is the authors' hope to alert biology teachers to this potential disparity and to underscore the importance of Bayes' formula in pedigree analysis and a wide range of other biological applications.Typical applications of the Bayesian method involve estimation of an unobservable parameter that describes an entire population using observable (objective) data derived by sampling techniques (Ledley, 1965).For example, a clinical trial might be designed to test the effectiveness of a drug in reducing the incidence of diabetes in a test group of individuals as compared with a control group of individuals who do not receive the drug, both groups being matched as closely as possible in all other respects (age, sex, lifestyles, health profiles, etc.).Bayesian methods are especially useful for analyzing more complex multivariate problems such as clinical trials designed to simultaneously gather data on two or more variables (e.g., age and drug treatment, or age, sex, and drug treatment).Awareness of so-called Bayesian statistics certainly is appropriate at the introductory college level.It also could be introduced at the high school level were it not for the fact that many biology teachers have been shortchanged in their formal statistical education.This unfortunate situation is likely to continue unless they receive help from sources like The American Biology Teacher.We believe our paper could be a first step toward providing the kind of help they need.In applying the information in this report, biology teachers should try to focus their students' attention on the fact that there often is more than one way to analyze biological data and that different analytical procedures may lead to different solutions, rather than focusing merely on the empirical results of a statistical analysis.They should also be made aware of the assumptions underlying the use of any statistical tool.For example, applying an analysis of variance to compare populations that do not roughly conform to normal distributions invalidates the results.Students should at least be made aware that there are