## Statistical Questions from the Classroom

Statistical Questions from the Classroom

by J. Michael Shaughnessy and Beth Chance

I was talking with a mathematically-astute friend of mine and told him I lacked confidence in my grasp of statistics. (Insert clever joke about confidence intervals here.) So he recommended this 88-page book published by the National Council of Teachers of Mathematics as a good refresher on some basic concepts. The book consists of 11 chapters, each one addressing a question frequently asked by statistics students. Continue reading “Statistical Questions from the Classroom”

## The Flaw of Averages

The Flaw of Averages: Why We Underestimate Risk in the Face of Uncertainty

by Sam L. Savage

This is a book about how to manage in a world of uncertainty. The beginning section presents a number of statistical concepts in simplified language; more sophisticated techniques follow. The author discusses how these concepts apply in a wide variety of contexts including oil exploration, pharmaceutical R&D, the stock market, the housing bubble, weather, climate change, health care, gene pools, the war of terror, and supply chains. He also describes some illogical accounting rules required by the FASB and the SEC. Continue reading “The Flaw of Averages”

## HBR Guide to Data Analytics Basics for Managers

HBR Guide to Data Analytics Basics for Managers

The objective of this book is to help managers make better data-driven decisions by working with data analysts and data scientists. The guide is a compendium adapted from 23 previously published Harvard Business Review and hbr.org articles.

“Framing a problem… is the most important stage of the analytical process for a consumer of big data. It’s where your business experience and intuition matter most. After all, a hypothesis is simply a hunch about how the world works. The difference with analytical thinking, of course, is that you use rigorous methods to test the hypothesis.”

## Chance

Chance: A Guide to Gambling, Love, The Stock Market, and Just About Everything Else

By Amir D. Aczel (1950-2015)

This is a book about probability, the “quantitative measure of the likelihood of a given event.” The author applies probability theory in numerous scenarios.

Assuming a World War II pilot had a 2% chance of being shot down on each mission, what are the chances of a pilot being shot down in 50 missions?  Nope—it is not 50 x 0.02. Using the law of unions of independent events, the answer is 1 – 0.9850 = 64%.  In another example, there are three overnight couriers with an on-time record of 90%, 88%, and 92% respectively. If someone sent an important document using all three services, what is the probability of at least one of them delivering on time? The answer is 1 – (0.10 x 0.12 x 0.08) = 99.904%.

“So what have we noticed here? Continue reading “Chance”

## Innumeracy

Innumeracy: Mathematical Illiteracy and its Consequences

by John Allen Paulos

Innumeracy refers to mathematical incompetence. Given the frequency of misleading social media memes that simply don’t add up, I’d say the book is as relevant today as it was when published in 1988.

“If the headline reads that unemployment declined from 7.1 percent to 6.8 percent and doesn’t say that the confidence interval is plus or minus 1 percent, one might get the mistaken impression that something good happened. Given the sampling error, however, the ‘decline’ may be nonexistent, or there may even be an increase.” Continue reading “Innumeracy”