By Lawrence J Hubert; Howard Wainer
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Additional info for A statistical guide for the ethically perplexed
0054. 90. Because we do not know whether a tumor is present, all we know is whether the test is positive, Bayes’ theorem must be used to calculate the probability we really care about, the Positive Predictive Value (PPV). All the pieces are available to use Bayes’ theorem to calculate this probability, and we will do so below. But first, as an exercise for the reader, try to estimate the order of magnitude of that probability, keeping in mind that cancer is rare and the test for it is only 90% accurate.
These skills in understanding are not “theoretical” in a pejorative sense, although they do require more thought than just being content to run the SPSS program blindly. They are absolutely crucial in developing both the type of reflective teaching and research careers we would hope to nurture in graduate students, and more generally for the quantitatively literate citizenry we would wish to be made up of our society. Graduate instruction in statistics requires the presentation of general frameworks and how to reason from these.
P. 128) Leo Breiman took on the issue directly of relying on stochastic models (or, as he might have said, “hiding behind”) in most of contemporary statistics. What Breiman advocates is the adoption of optimization in place of parameter estimation, and of methods that fall under the larger rubric of supervised or unsupervised statistical learning theory. , 2009) (T. Hastie, R. Tibshirani, & J. Friedman). We give the abstract from Leo Breiman’s Statistical Science article, “Statistical Modeling: The Two Cultures” (2001, 16, 199–215): There are two cultures in the use of statistical modeling to reach conclusions from data.