Statistics

RStatistics is an area of mathematics, a collection of tools for analyzing data, and a way of thinking. As a subset of mathematics, statistics can be the study of multidimensional space, models of chance, or representational structure and change. For most people, statistics is more practical.

Most see statistics as a collection of procedures in a stat. program: you push the button and out comes the answer. Descriptive statistics helps summarize a variable by finding the most representative score (mode, median or mean). It also describes how diverse the scores are. Inferential statistics goes beyond describing. It uses patterns of numbers to infer the relationships between variables. Researchers predictions, forecasts and decisions based on these patterns.

But statistics is at its best as a way of thinking. We live in a world of freedom. Things are not set but can change. In a broad sense, this independence of events can be seen as uncertainty. We know the sun will come up tomorrow (certainty) but we don’t what our day will hold (uncertainty). This uncertainty doesn’t bother us because we believe we can handle the circumstances of life as they come.

In general, people are not good at handling uncertainty. So we generally ignore it, and assume that life is stable. We accept that we sometimes fall, run into things with our cars, and get sick. We accept, at least in ourselves, that these events are chance: they are not the result of goblins, dragons or unicorns. But we’re less willing to accept that intelligence, running, and musical ability are randomly distributed. Statistical thinking is applying logic to life. It is using the scientific method to better understand life’s uncertainty.

Here is a catalog style description of the course:

Introductory course in descriptive and inferential statistics. Special attention given to data description, probability and the normal curve. Topics include critical intervals, hypothesis testing, goodness of fit and factorial analysis. Technology is used to analyze data sets.

Here is what it really means:

This course is all about planning, thinking and interpreting. Number crunching isn’t as important as thinking.

Let’s start with some basic principles.