Jeff,
I am not overly familiar with basic texts on these subjects. But in my experience all seem to suffer from a failure to understand the ways measure employed to analyze differences in outcome rates tend to be affected by the frequency of an outcome. Inasmuch as the rate ratio and its associated relative difference are among the more fundamental measures used in analyses of health issues, I note in particular the (a) pattern whereby the rarer an outcome the greater tends to be the relative difference in experience and the smaller tends to be the relative difference in avoiding it, and (b) the corollary pattern whereby a factor that affects an outcome rate tends to cause a larger proportionate change in the rate for the group with the lower baseline rate while causing a larger proportionate change in the opposite outcome rate for the other group. Further, the rate ratio is not only an unsound, but illogical, measure of association given that when a rate ratio is the same with regard to different baseline rates it is necessarily different with regard to the opposite outcome rates.
Failure to understand the above and related patterns has undermined virtually all health disparities research as well as all subgroup analyses that rely on the assumption that departure from a constant rate ratio as indicative of a subgroup effect.
I have posted a lot of material on ASA Connect regarding these issues. Below are a few references. The is a letter urging ASA it to form a committee to address these issues. See especially pages 339-341 of reference 2 regarding the way observers draw inferences based on the comparative size of the relative difference they happening to be examining without understanding the reasons to expect the observed pattern to occur most of the time and without recognizing that the relative difference to for the opposite outcome commonly would support an opposite conclusion.
Irrespective of the validity of the broader points in the reference, it seems to me that a course on statistical literacy and reason should at least communicate that (a) there are two relative differences; (b) the two relative differences will commonly change in opposite directions as the prevalence of an outcome changes; (c) anytime a relative difference and an absolute difference have changed in opposite direction, the other relative difference will necessarily have changed in the opposite direction of the first relative difference and the same direction as the absolute difference. I am not sure than any standard text will communicate these things.
Jim Scanlan
1.Letter to American Statistical Association (Oct. 8, 2015) http://jpscanlan.com/images/Letter_to_American_Statistical_Association_Oct._8,_2015_.pdf
2. “Race and Mortality Revisited,” Society (July/Aug. 2014) http://jpscanlan.com/images/Race_and_Mortality_Revisited.pdf
3. “The Mismeasure of Health Disparities,” Journal of Public Health Management and Practice (July/Aug. 2016)http://www.jpscanlan.com/images/The_Mismeasure_of_Health_Disparities_JPHMP_2016_.pdf
4. “The Mismeasure of Health Disparities in Massachusetts and Less Affluent Places,” Quantitative Methods Seminar, Department of Quantitative Health Sciences, University of Massachusetts Medical School (Nov. 18, 2015)
Abstract: http://jpscanlan.com/images/UMMS_Abstract.pdf
PowerPoint: http://jpscanlan.com/images/Univ_Mass_Medical_School_Seminar_Nov._18,_2015_.pdf
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James Scanlan
James P. Scanlan Attorney At Law
Original Message:
Sent: 07-12-2016 14:47
From: Jeff Gates
Subject: Needing insights regarding statistical literacy and reasoning
Hi all,
I've been asked to create an intermediate level "statistical literacy and reasoning" 10-week foundation course for health science graduate students (....intending to take other applied stats courses later).
Does anyone have a suggestion for a textbook (and assessments) for such a course? I'm more familiar with integrating literacy and reasoning into my regular applied courses, not a stand-alone type format.
Thanks for any insights!
Jeff Gates, DrPH
Research Faculty