Statistics In A Nutshell

What is statistics?

Statistics 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.

Major Approaches

The three major approaches to statistics are formulaic, calculation and conceptual. The first approach tries to teach you how one formula is derived from another. Although presented as logic, it often relies more on authority (take my word for it). The calculation approach gives you a cookbook, doesn’t require you to think, and expects you to dislike mathematics. For many, this is their only exposure to statistics, and usually results in students being more convinced about the stupidity of statistics than before they began. The third approach emphasizes the importance of assumptions, the selection of procedures, and the application of logic.

Major Theorists

Bayes, Thomas
Cattell, Raymond
Fermat, Pierre de
Fischer, R.A.
Fourier, Joseph
Galton, Francis
Gauss, Carl
Gosset, William (“student”)
Graunt, John & Petty, William
Mann & Whitney
Pascal, Blaise
Pearson, Karl
Spearman, Charles
Stevens, Stanley
Tukey, John 

Additional Information
     For more on statistics, check out my 10-Day Guided Tour of Statistics.

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