# Ch 1. What’s the Point?

What is the point? The point is to do math, or to dazzle friends and colleagues with advanced statistical techniques. The point is to learn things that inform our lives.

– Charles Wheelan

[PREFACE: I purchased Naked Statistics by Charles Wheelan many years ago, thinking its an important book to add to any Math Teacher’s arsenal (and it is!) but had only gotten through the first three chapters before dismissing it for another read. It is not a boring book – quite the opposite in fact – but I felt that mere passive reading was not enough for me to really retain the important ideas and intuition that Wheelan is trying to impart to his readers. This time, I’m giving it another chance and plan to summarize material I am learning, relate it to my own experiences, and share that learning here on my blog.]

I wrote about why statistics matters in a previous post. Here, I continue to elaborate on the point as I summarize my biggest takeaways from the first chapter. This chapter provided an overview of big ideas in statistics that we’ll be learning about throughout the book.

Description and Comparison
Descriptive statistics is like creating a zip file, it takes a large amount of information and compresses it into a single figure. This figure can be informative and yet completely striped of any nuance. Like any statistical tool, one must be careful of how and when we employ such figures and the implications it might have on the audience.

So a descriptive statistic is a summary statistic. Let’s start with one that many of you may already be familiar with – GPA. Let’s say a student graduates from university with a GPA of 3.9. What can we make of this? Well, we might be able to discern that on a scale from 0 – 4.0 a GPA of 3.9 is pretty darn high. But some universities grade on a scale of 0 – 4.3, accounting for a grade of A+. What this simple statistic doesn’t tell us is what program did the student graduate from? Which school did they attend? Did they take courses that were relatively easy or difficult? How does this grade compare with others in the same program? Wheelan writes, “Descriptive statistics exist to simplify, which implies some loss of nuance or detail (6).”

Inference
We can use statistics to draw conclusions about the “unknown world”  from the “known world.” More on that later.

Assessing Risk and Other Probability Related Events
Examples here include using probability to predict stock market changes, car crashes or house fires (think insurance companies), or catch cheating in standardized tests.

Identifying Important Relationships
Wheelan describes the work of identifying important relationships as “Statistical Detective Work” which is as much an art as it is a science. That is, two statisticians may look at the same data set and draw different conclusions from it. Let’s say you were asked to determine whether or not smoking causes cancer? How would you do it? Ethically speaking, running controlled experiments on people may prove unfeasible, for obvious reasons.

An example Wheelan offers here goes something like this:
Let’s say you decide to take a few shortcuts and rather than expending time and energy into looking for a random sample, you survey the people at your 20th high school reunion and look at cancer rates of those who have smoked since graduation. The problem is that there may be other factors distinguishing smokers and nonsmokers other than smoking behaviour. For example, smokers may tend to have other habits like drinking or eating poorly that affect their health. Smokers who are ill from cancer are less likely to show up at high school reunions. Thus, the conclusions you draw from such a data set may not be adequate to properly answer your question.

In short, statistics offers a way to bring meaning to raw data (or information). More specifically, it can also help with the following:

• To summarize huge quantities of data
• To make better decisions
• To recognize patterns that can refine how we do everything from selling diapers to catching criminals
• To catch cheaters and prosecute criminals
• To evaluate the effectiveness of policies, programs, drugs, medical procedures, and other innovations
• To spot the scoundrels who use these very same powerful tools for nefarious ends

(Wheelan 14)

Lies, damned lies, and statistics.

– Mark Twain