A good book for basic statistical thinking and caution is "How to Lie with Statistics" (1950) by Darrell Huff. I recommend the book and its ideas. However, I recently learned that Huff was paid by tobacco companies to assist in obscuring the answer to the question of damage done to our bodies by smoking. He worked for the tobacco companies, which are known to have gone to great lengths to assure everyone that cigarettes were harmless. Nowadays, being overweight and smoking are two factors that are first mentioned in discussions of unhealthful practices.
One of the best books for raising red flags and surprising the reader with the way the world works is "The Improbability Principle" (2014) by David Hand. The book is subtitled "Why Coincidences, Miracles and Rare Events Happen Every Day". The basic idea of the book is that if the same thing is repeated many, many times, very strange outcomes can be observed. One of the events Prof. Hand discusses is this one:'
Another, rather frustrating, way in which the law of combinations can generate lottery matches is illustrated by what happened to Maureen Wilcox in 1980. She bought tickets containing the winning numbers for both the Massachusetts Lottery and the Rhode Island Lottery. Unfortunately for her, however, her ticket for the Massachusetts Lottery held the winning numbers for the Rhode Island Lottery, and vice versa. If you buy tickets for ten lotteries, you have ten chances of winning. But ten tickets mean 45 pairs of tickets, so the chance that one of the ten tickets will match one of the ten lottery draws is over four times larger than your chance of winning. For obvious reasons, this is not a recipe for obtaining a vast fortune, since matching a ticket for one lottery with the outcome of the draw for another wins you nothing—apart from a suspicion that the universe is making fun of you.
Another David Hand book is "Dark Data", where he discusses difficulties with data, such as bias toward or away from some important factor that matters but we are unaware of.
We hear much about data and evidence these days. Of course there can
be intentional misleading going on but even when there isn't, data can be ambiguous or unconvincing.
