Double Your Variance, Dirtify Your Bayes, Devour Your Pufferfish, and Draw your Kidstrogram
Volume 1, Issue 1 (2023), pp. 4–23
Pub. online: 5 October 2022
Type: Statistical Methodology
Open Access
Open Access
Accepted
1 September 2022
1 September 2022
Published
5 October 2022
5 October 2022
Abstract
This article expands upon my presentation to the panel on “The Radical Prescription for Change” at the 2017 ASA (American Statistical Association) symposium on A World Beyond $p<0.05$. It emphasizes that, to greatly enhance the reliability of—and hence public trust in—statistical and data scientific findings, we need to take a holistic approach. We need to lead by example, incentivize study quality, and inoculate future generations with profound appreciations for the world of uncertainty and the uncertainty world. The four “radical” proposals in the title—with all their inherent defects and trade-offs—are designed to provoke reactions and actions. First, research methodologies are trustworthy only if they deliver what they promise, even if this means that they have to be overly protective, a necessary trade-off for practicing quality-guaranteed statistics. This guiding principle may compel us to doubling variance in some situations, a strategy that also coincides with the call to raise the bar from $p<0.05$ to $p<0.005$ [3]. Second, teaching principled practicality or corner-cutting is a promising strategy to enhance the scientific community’s as well as the general public’s ability to spot—and hence to deter—flawed arguments or findings. A remarkable quick-and-dirty Bayes formula for rare events, which simply divides the prevalence by the sum of the prevalence and the false positive rate (or the total error rate), as featured by the popular radio show Car Talk, illustrates the effectiveness of this strategy. Third, it should be a routine mental exercise to put ourselves in the shoes of those who would be affected by our research finding, in order to combat the tendency of rushing to conclusions or overstating confidence in our findings. A pufferfish/selfish test can serve as an effective reminder, and can help to institute the mantra “Thou shalt not sell what thou refuseth to buy” as the most basic professional decency. Considering personal stakes in our statistical endeavors also points to the concept of behavioral statistics, in the spirit of behavioral economics. Fourth, the current mathematical education paradigm that puts “deterministic first, stochastic second” is likely responsible for the general difficulties with reasoning under uncertainty, a situation that can be improved by introducing the concept of histogram, or rather kidstogram, as early as the concept of counting.
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