Introduction to Statistical Methods

Reading Assignment

Chapter 1; Sections Covered: 1-4 Read the first four sections on this chapter. There's nothing much here to challenge you. It is an attempt to orient the reader generally to the subject of statistics. Generally these "orientations" (like "outlines" of papers you are attempting to write) do not help a beginning student because they make little sense until after the subject has been learned. To some, they belong in the category of things that are COIK, i.e., Clear Only If Known. The more important notion to be got across at this early stage is how the subject of statistical methods is organized. This diagram may help:

Statistical methods has two major branches: Descriptive and Inferential . The first half of this course will deal with Descritptive Statistical Methods; the second half, with Inferential Statistical Methods.

Descriptive Statistics

Example: "The average income of the 104 families in our company is $28,673."

In descriptive statistics, our objective is to describe the properties of a group of scores or data that we have "in hand," i.e., data that are accessible to us in that we can write them down on paper or type them into a spreadsheet. In descriptive statistics we are not interested in other data that were not gathered but might have been; that is the subject of inferential statistics.

What properties of the set of scores are we interested in? At least three: their center, their spread, and their shape. Consider the following set of scores, which might be ages of persons in your bridge club:

28, 38, 45, 47, 51, 56, 58, 60, 63, 63, 65, 66, 66, 67, 68, 70

We could say of these ages that they range from 28 to 70 (spread), and the middle of them is somewhere around 60 (center). Now their shape is a property of a graph that can be drawn to depict the scores. If I marked the scores along a number line, like so

then we can see that the ages tend to bunch at the older ages and trail off very gradually for the younger ages. Later we will learn that this distribution of data is said to be negatively skewed, because the "trailing off" is toward the negative end of the number line.

Inferential Statistics

Example: "This sample of 512 families from Maricopa county indicates with 95% confidence we can conclude that the average family income in the county is between $25,187 and $29,328."

In inferential statistics, our interest is in large collections of data that are so large that we can not have all of them "in hand." We can, however, inspect samples of these larger collections and use what we see there to make inferences to the larger collection. How samples relate to larger collections of data (called populations) from which they have been drawn is the subject of inferential statistical methods. Inferential statistics are frequently used by pollsters who ask 1000 persons whom they prefer in an election and draw conclusions about how the entire state or county will vote on election day. Scientists and researchers also employ inferential statistics to make conclusions that are more general than the conclusions they could otherwise draw on the basis of the limited number of data points they have recorded.

Test over the above concepts.