Make no mistake, statistics is hard.

Many people use statistics informally in their lives daily. Sometimes, these people use statistics without understanding it fully.

Maybe you are someone who works in with data and statistics, and don’t have the concepts and assumptions nailed down.

Would your job be easier if you knew these concepts? Would it be valuable if you had simple explanations and stories for why different statistical concepts make sense?

What if you could learn to think statistically, and apply the concepts of statistics appropriately?

Thinking Statistically, by Uri Bram, teaches you to think like a statistician and understand at a high level some of the big concepts of statistics.

Thinking Statistically looks to help you understand three powerful concepts of statistics using every day language and examples.

Far from a textbook, Thinking Statistically is an easy and enjoyable read which will lead towards success when using statistics in your daily life.

The rest of this post includes a summary of Thinking Statistically, takeaways from Thinking Statistically, and a reading 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

## Book Summary of Thinking Statistically

Thinking Statistically teaches you to think like a statistician without worrying about the formal statistical techniques.

Thinking Statistically discusses three main concepts. The best part of the book is it does so *without* using **equations or scary math. **Instead of equations (which the author purposely stays away from), every day language and stories are used to discuss these concepts.

Staying away from the details helps make this book more digestible for the average reader.

Concepts and abstractions can be useful. You don’t always need to know the details backing them up.

There are three concepts which Thinking Statistically touches on:

**Selection Bias****Endogenity****Bayes’ Theorem**

Let’s go into more detail on each of these statistical concepts.

### Thinking Statistically about 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.

### Thinking Statistically about 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 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.

### Thinking Statistically about 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 Bayes’ theorem, a person’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, but the thoughts presented in the book were good enough for everyday uses.

## Takeaways from Thinking Statistically

With every book you read, it is a must to have takeaways and actionable items to implement in life.

The main takeaway from Thinking Statistically is **be careful** when:

**presenting data****making assumptions on a population of data****thinking about what could explain a certain event.**

There is so much data around us. With so much data, there will also be a lot of noise. Removing that noise, and understanding the trend will be step one of getting to the details, and step two will be applying these statistical concepts to understand more fully the problem.

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…

By understanding the data, understanding the assumptions and models, and thinking statistically, you will be able to more accurately understand complex situations.

“There are three kinds of

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

## Our Recommendation for Thinking Statistically

Thinking Statistically is less than 100 pages long, and is a quick read. Thinking Statistically is also quite enjoyable, as the author has a number of silly comments scattered throughout the book. In addition, there are some pictures, and various stories to back up real life events where people made false judgments when working with data.

Thinking Statistically is fine book for increasing your understanding about statistics, and the concepts and theories of selection bias, endogenity and Bayes’ Theorem.

If you are looking to learn more about statistics, definitely check out Thinking Statistically.

*Readers: do you use statistics on a daily basis? Do you follow the concepts above in your thought processes?*