This article suggests looking at some well-known statistics problems will “change the way you see the world.” Enjoy the Monty Hall problem, the birthday paradox, gambler’s ruin, Abraham Wald’s memo, and Simpson’s paradox.
Here is what is missing from this article: explaining how statistics is helpful beyond these five particular cases. How would statistics help in a different situation? What is the day-to-day usefulness of statistics? I would suggest several things:
1. Statistics helps move us away from individualistic or anecdotal views of reality and toward a broader view.
2. Statistics can encourage us to ask questions about “reality” and look for data and hidden patterns.
3. Knowing about statistics can help people decipher the numbers that see every day in news stories and advertisements. What do survey or poll results mean? What numbers can I trust?
Tackling these sorts of issues would be much better for the public than looking at five fun and odd applications of statistics. Of course, these three points may not be as interesting as five statistical brain teasers but these five cases should be used to point us to the larger issues at hand.
A mathematician thinks about the differences between stories and statistics and the people who prefer one side over another:
Despite the naturalness of these notions, however, there is a tension between stories and statistics, and one under-appreciated contrast between them is simply the mindset with which we approach them. In listening to stories we tend to suspend disbelief in order to be entertained, whereas in evaluating statistics we generally have an opposite inclination to suspend belief in order not to be beguiled. A drily named distinction from formal statistics is relevant: we’re said to commit a Type I error when we observe something that is not really there and a Type II error when we fail to observe something that is there. There is no way to always avoid both types, and we have different error thresholds in different endeavors, but the type of error people feel more comfortable may be telling. It gives some indication of their intellectual personality type, on which side of the two cultures (or maybe two coutures) divide they’re most comfortable. I’ll close with perhaps the most fundamental tension between stories and statistics. The focus of stories is on individual people rather than averages, on motives rather than movements, on point of view rather than the view from nowhere, context rather than raw data. Moreover, stories are open-ended and metaphorical rather than determinate and literal…
I’ll close with perhaps the most fundamental tension between stories and statistics. The focus of stories is on individual people rather than averages, on motives rather than movements, on point of view rather than the view from nowhere, context rather than raw data. Moreover, stories are open-ended and metaphorical rather than determinate and literal.
This is a good discussion and one that I think about often while teaching statistics or research methods. Stories are often easy for students to grab unto, particularly if told from an interesting point of view. In the end, these stories (particularly the “classics”) have the ability to illuminate the human condition or interesting concerns but don’t have the same ability to offer more concrete overviews of the typical or common experience. Statistics do offer a different lens for viewing the world, one where individual experiences are muted in favor of data about larger groups. Both can miss important features of the reality around us but offer different angles for tackling similar concerns.
Both have their place and I would suggest both are necessary.