Concepts and abstractions are often useful even if you don’t know the details underneath them. For example, in finance, it is beneficial to understand the effects on the economy if the Central Bank raises interest rates, but you don’t need to know the inner-workings of how the Central bankers actually do it. Most people use statistics informally in their lives daily. Thinking Statistically, by Uri Bram, teaches you to think like a statistician without worrying about the formal statistical techniques.

I picked up Thinking Statistically, because I work as a quantitative analyst (aka statistician) in my day job. Given that I’m paid to perform statistical analysis, I figured it might be good if I read a book called Thinking Statistically ðŸ™‚ In addition, I enjoy reading books which help in solidifying my understanding of the concepts behind the details. If I can’t break it down to an elementary school level, then my understanding might not be the best.

The rest of this post will cover a summary of Thinking Statistically, my takeaways, and my recommendation for you.

“The sexy job in the next 10 years will be statisticians… and I’m not kidding.” – Hal Varian, Chief Economist of Google

## Summary of Thinking Statistically

As mentioned above, Thinking Statistically teaches you to think like a statistician without worrying about the formal statistical techniques. There are three concepts Thinking Statistically touches on:

- Selection Bias
- Endogenity
- Bayes Theorem

### Selection Bias

Selection bias is everywhere, and creeps up on us whenever we take a non-random sample and act if it were random. Some data is so sneaky that it biases itself: whether or not a particular piece of data arrives in your final sample is dependent on the value that datum would’ve taken.

One of the examples in Thinking Statistically was how selection bias caused pollsters to miss-call President Truman’s re-election. In 1948, the polls were taken over the phone. Guess who had phones in the 40’s? The rich Republican leaning people – not the Democrats. As a result, all the polls thought the Republican candidate was the most popular candidate. This was far from the truth – President Truman won re-election with ease.

### Endogenity

Endogenity problems occur whenever the supposedly-random error term turns out to be correlated with a variable in your model, or with one that should’ve been in your model, but wasn’t. For an example, most models will take the form Y = X + intercept + random error term. Essentially, if you are looking to model a certain event or probability, you want to include all relevant variables in your model. If you don’t include all relevant variables, you could have some issues with prediction.

One of the examples in Thinking Statistically on endogenity is how college GPA is completely useless as a measure of a student’s ability. Many of us think college GPA can be expressed as a function of effort and ability. Though, one factor we are leaving out is the difficulty of the coursework for a given student. If you leave out the difficulty of courses taken, you expose yourself to endogenity problems.

### Bayes’ Theorem

Bayes’ Theorem describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if cancer is related to age, then, using Bayesâ€™ theorem, a personâ€™s age can be used to *more accurately* assess the probability that they have cancer, compared to the assessment of the probability of cancer made without knowledge of the person’s age. Thinking Statistically didn’t do the best job of explaining Bayes’ Theorem (it’s a complex theorem and I don’t know how I would approach it to be honest…) I will leave it to you to explore more or you can ask questions in the comment section below.

Thinking Statistically is less than 100 pages long and was a quick read. There were some pictures, and stories to back up real life events where people made false judgements when working with data. In addition, the author has some fairly funny comments scattered throughout the text.

## My Takeaways

With all books I read, I look to have a few takeaways and action steps to apply in my life. With Thinking Statistically, I knew the concepts presented in the book well, and as a result, there are no direct applications to my life.

One point I will make is **I should always be careful** when presenting data, making assumptions on a population of data, or thinking about what could explain a certain event. There is so much data around us. Turn on the news and you will here various statistics on different studies occurring down at your local university. Just make sure to be careful when looking at a study or some research. You can lie with statistics very easily…

“There are three kinds of

lies:lies, damnedlies, andstatistics.” – British Prime Minister Benjamin Disraeli

## My Recommendation

Thinking Statistically is just fine for the author’s purpose – it’s a short read, is interesting, and brings up some decent points on statistical thinking. The author is pretty funny and has a lot of tongue and cheek comments, so it is enjoyable as well. I would recommend Thinking Statistically if you produce statistical analysis on a regular basis or manage statisticians. Otherwise, if you are looking to re-train your mind, I’d recommend Blink (book review) or Think Like a Freak (book review).

Do you use statistics on a daily basis? Do you violate some of the concepts above in your thought processes? What books have you enjoyed reading which are about thinking?

Erik

## Comments 2

You lost me at Statistically….but I did like Blink! ðŸ™‚

Author

ðŸ™‚ ha, yeah… I’m a nerd!