Parameter. A parameter is a result based on enumeration of a population. Because enumeration is seldom undertaken, parameters generally are not known. Instead, using methods we describe in Part 4, statistics from a sample are used to estimate the values of parameters.

Sample design. This is the plan prepared in advance for selecting a sample, using a probability or nonprobability method. A properly described sample design includes:

• A precise definition of target population;
• Definition of the sampling element (defined a bit later);
• Description of the sampling frame used (also defined later);
• Description of the method of sample selection;
• The planned size of the sample;
• The time period during which data were obtained; and
• The size and composition of the actual sample that was obtained.

Other social scientists judge the adequacy of a sample using these criteria. You should include all the elements listed above in the description of any sample design you use.

Selecting or drawing a sample. This is the process of selecting sampling elements from a sample frame using a probability or nonprobability method.

Sampling error. This is a mathematical term that describes how well a statistic for a given sample provides an estimate of the corresponding parameter. Chapter 19 describes how to calculate the sampling error for a mean (average).

A number of Web sites define and illustrate the terms we just defined. One site you might find helpful is: Sampling Terminology.

With this background, we now turn to four ways for selecting probability samples. These are the:

• Simple random sample;   
• Systematic random sample;
• Stratified random sample and;
• Cluster or multiple stage sample.  

Each has its specific uses. We begin with the basic and simplest of these — the simple random sample.

Simple random sample

An illustration should help you grasp the concept of a simple random sample. Imagine we wanted a probability sample of 100 faculty members out of a population of 500. One way to get the sample would be to write the name of each faculty member on a slip of paper, put the slips in a box, shake the box until the slips are thoroughly mixed, and then reach in and draw out a slip of paper. This would result in the random or chance selection of the first faculty member of our sample of 100. The selected name would be written down and that person would become a member of the sample. This process would be repeated 99 times. Each time a slip of paper is drawn, all the remaining pieces or names have had an equal chance of being selected. This is the basis of a simple random sample.

Selecting

Steps in selecting a simple random sample are:

1. Define the target population and sampling element;
2. Select a sampling frame; and
3. Select the sample.