Statistical Inference: A Short Course

1.1 Statistics Defined

Broadly defined, statistics involves the theory and methods of

collecting,

organizing,

presenting,

analyzing, and

interpreting

data so as to determine their essential characteristics. While some discussion will be devoted to the collection, organization, and presentation of data, we shall, for the most part, concentrate on the analysis of data and the interpretation of the results of our analysis.

How should the notion of data be viewed? It can be thought of as simply consisting of “information” that can take a variety of forms. For example, data can be numerical (test scores, weights, lengths, elapsed time in minutes, etc.) or non-numerical (such as an attribute involving color or texture or a category depicting the sex of an individual or their political affiliation, if any, etc.) (See Section 1.4 of this chapter for a more detailed discussion of data forms or varieties.)

Two major types of statistics will be recognized: (1) descriptive; and (2) inductive¹ or inferential.

Descriptive Statistics: Deals with summarizing data. Our goal here is to arrange data in a readable form. To this end, we can construct tables, charts, and graphs; we can also calculate percentages, rates of change, and so on. We simply offer a picture of “what is” or “what has transpired.”

Inductive Statistics: Employs the notion of statistical inference, that is, inferring something about the entire data set from an examination of only a portion of the data set. How is this ...