Reflection of calculated risk by Gred Gigerenzer - Book Report/Review Example

Reflection on the book The author is critical about the lack of understanding the meaning of numerical thinking. The German scientist opines that although most of the children in western countries learn reading and writing quite efficiently, but they lack to think in terms of statistics, even during their adulthood. Gigerenzer has termed this as “innumeracy”, which he describes as the inability to think logically, based on reasoning, about uncertainties and risks. In the book, Gigerenzer offers advice for all professionals involved in seeking the certainty with the help of numbers.

The author has particularly traced many case studies, concerning medical profession that involved screening and other tests. Interpretation of figures This book lays great emphasis on the need to learn statistics for people who are in the field of medical counseling, DNA finger printing, while interpreting mathematical principals regarding frequency and risk as applied to daily life activities. For example, the author has described the true story of a psychiatrist who prescribed ‘prozac’ medicine to a patient. . Link to statistics in the medical field Numerical interpretation of Baye’s rule The interpretation of this rule has caused the confusion, while trying to find the accuracy of screening tests like mammography and HIV.

The author has given an example regarding this, in the book, while discussing the accuracy of a test meant for detection of breast cancer. According to the book, if women above the age of 40 are put on a mammography test, the correct interpretation of the positive test is 90 percent, while the same for negative test is 93 percent. When discussing with the doctor about the accuracy of the test results, it is assumed that the same are 90 percent accurate for the patients who are positive for breast cancer, while these are 93 percent accurate for the patients who test negative for breast cancer.

The author opines that such interpretation using conditional probabilities is incorrect. Instead, natural frequencies should be used for accurate interpretation of Baye’s rule. In addition, if the breast cancer chances in women are .8%, which would mean eight women out of 1000 have such cancer, then only seven females will have true positive mammography results. Applying further the principals of natural frequencies, the results will be quite different from earlier calculations based on conditional probabilities.

However, the patient would need taking three consecutive tests for being more than 90 percent certain of a positive breast cancer. Similarly, the book advises, taking two or three consecutive tests, in case of HIV or prostrate cancer is better method of ensuring accuracy (Gigerenzer (1)). Understanding risk According to Gigerenzer, doctors and other professionals have the tendency of