# Statistics I:  Probability, Description, and Simple Test of Relationship

Much of the information you will need in attending to the public’s business is unique—it depends on the individual characteristics of a specific situation.  You might want to know whether a proposed construction is fifty feet from the lot line, or if someone’s dog is barking outside at night, or whether your assistant is going to get that report to the committee on time for Monday’s meeting.  You don’t need fancy quantitative analysis for situations like these; the facts speak for themselves.  While the solution may be far from straightforward, the problem at least can be described fairly simply.

Some problems are not so simply described.  It might seem that one neighborhood in the city is getting “run down.”  You seem to have noticed more houses needing paint—but how many more?  And is that “enough” to mean that there is a problem?  Or you might wonder if the population in the region is getting older—maybe it seems that you are seeing fewer babies around lately.  Both of these situations cannot be satisfactorily described by simple observation, because the really interesting information is what is going on between the observations or what is going on beyond the scope of any single observation.

Fortunately (or unfortunately, if you prefer the simple life), there are tools which can be used to summarize a large body of observations and which can be used to compare these summaries to other, similar summaries.  You are probably already familiar with some of them, like “average” and “correlation” (as in, “there is a relationship between smoking and lung cancer”).  Others have exotic names, like “Student’s t-Test” and “Chi-square.”  All of these tools are jointly known as “statistics,” a word coined in the eighteenth century to describe information which was being collected and analyzed about affairs of state.  Since then, statistics have spread to fields other than public administration, but the name remains to remind us of their importance in making sense of the public’s business.