Introduction to Statistics Through Resampling Methods and R, 2nd Edition

Chapter 1

Variation

If there were no variation, if every observation were predictable, a mere repetition of what had gone before, there would be no need for statistics.

In this chapter, you’ll learn what statistics is all about, variation and its potential sources, and how to use R to display the data you’ve collected. You’ll start to acquire additional vocabulary, including such terms as accuracy and precision, mean and median, and sample and population.

1.1 VARIATION

We find physics extremely satisfying. In high school, we learned the formula S = VT, which in symbols relates the distance traveled by an object to its velocity multiplied by the time spent in traveling. If the speedometer says 60 mph, then in half an hour, you are certain to travel exactly 30 mi. Except that during our morning commute, the speed we travel is seldom constant, and the formula not really applicable. Yahoo Maps told us it would take 45 minutes to get to our teaching assignment at UCLA. Alas, it rained and it took us two and a half hours.

Politicians always tell us the best that can happen. If a politician had spelled out the worst-case scenario, would the United States have gone to war in Iraq without first gathering a great deal more information?

In college, we had Boyle’s law, V = KT/P, with its tidy relationship between the volume V, temperature T and pressure P of a perfect gas. This is just one example of the perfection encountered there. The problem was we could never quite duplicate this (or ...