Reviews - What do customers think about Christian and Humanist Foundations for Statistical Inference: Religious Control of Statistical Paradigms?
Christian and Humanist Foundations for Statistical Inference: Religious Control of Statistical Paradigms Oct 11, 2009
Hartley's book rigorously treats an important issue regarding biases in various statistical inference paradigms. The influence of biases is significant in many scientific enterprises. The bottom line is that religious beliefs (including humanism) "set bounds for overviews of reality which, similarly, set bounds for scientific theorizing." In other words, biases have a bearing on the questions asked in scientific endeavors and the interpretation of data gathered during observation and experimentation. Moreover, some biases have negative effects on the ability to draw correct conclusions from data. As noted by the author, "Whether or not we are at all explicit about religious beliefs, through our overviews of reality, they impact our scientific activities." And, "Each [statistical] paradigm influences what calculations will be performed, and determines how the results of those calculations will be interpreted."
Hartley has produced an extremely well-referenced and well-reasoned work. It includes a review of various paradigms used for statistical inference and a summary of the Philosophy of the Law Idea that is used to assess the strengths and weaknesses of each paradigm's overview of reality. His presentation of each paradigm includes direct quotes from respective advocates. In the book, the central question of statistical inference is defined as "Given observed quantitative data, how credible is a scientific hypothesis of interest?" For good reason, the scientific community asks, `What does a given set of data say about reality.' What we don't ask often enough is, `What does the data not say?' When the set of questions asked are not complete or appropriate, overstatement of claims is often made.
Examples are given in the book of how unjustified inferences are often made about hypotheses, given data, even though the necessary information to do this is not available. In these cases, inferences should only be made about the data itself and not overstated claims about hypotheses. One reason for this error is that one's worldview influences the available or allowable inferences. Comparing two categories of statistical paradigms, the author states that "Frequentist `answers' are frequencies of data, whereas Bayesian answers are certainties regarding hypotheses." "Direct and indirect frequentism calls on the statistician to reinterpret frequencies of data given hypotheses, as if they were statements about hypotheses given data."
It is easy to ignore the need to acquire necessary information, such as establishing probabilities of prior distributions (pre-analytic probability distributions of statistical parameters), but "Not only are prior probabilities needed to make inferences about hypotheses; they are almost always needed even to evaluate the evidentialists' type of evidence." Referring to the influence of human investigators in statistical inference, the author states that "unlike indirect frequentism, subjective bayesianism relies on scientific `objects' to place fiduciary `limitations' on `the subject who does the knowing.'" In layman's terms, bayesianism addresses "the inductive question, `What have I learned concerning my hypothesis from this experiment?' rather than the frequentist question, `What would happen if I repeated this experiment many times?'"
The author concludes that "Both direct and indirect frequentism have ignored the basic difficulty that their statistical results (frequencies of data) are deductive statements, rather than the inductive statements that would constitute inference." This book is not an easy read for those without some statistical understanding, but the points made by the author are well worth knowing and heeding when conducting scientific research.
Some brief comments Feb 28, 2009
The author has included a tribute to me in the Acknowledgments. In normal circumstances that might preclude me from writing a review. Nevertheless, I write this to say that my hopes in encouraging Andrew Hartley as he wrote this book have been amply fulfilled. Here is a book that will help those who study it to make sense of statistics. It is helping me re-examine the place of statistics in the social sciences. It can assist scholars from all sciences, the humanities and other areas of scholarship to examine the validity and limits of statistical contributions to science while also exploring the various attempts to justify the science or make all disciplines subject to its peculiar rigours. Andrew rightly identifies the religious drives that are implicit in the various "statistical paradigms". He makes a very creditable start to developing statistical from the standpoint of the philosophy of the law idea. This is the Christian philosophy that was initiated by Herman Dooyeweerd and promoted these days by a diverse bands of scholars found in many places around the globe.