Populations, Samples, Parameters, and Statistics
The field of inferential statistics enables you to make educated guesses about the numerical characteristics of large groups. The logic of sampling gives you a way to test conclusions about such groups using only a small portion of its members.
A population is a group of phenomena that have something in common. The term often refers to a group of people, as in the following examples:
- All registered voters in Crawford County
- All members of the International Machinists Union
- All Americans who played golf at least once in the past year
But populations can refer to things as well as people:
- All widgets produced last Tuesday by the Acme Widget Company
- All daily maximum temperatures in July for major U.S. cities
- All basal ganglia cells from a particular rhesus monkey
Often, researchers want to know things about populations but do not have data for every person or thing in the population. If a company's customer service division wanted to learn whether its customers were satisfied, it would not be practical (or perhaps even possible) to contact every individual who purchased a product. Instead, the company might select a sample of the population. A sample is a smaller group of members of a population selected to represent the population. In order to use statistics to learn things about the population, the sample must be random. A random sample is one in which every member of a population has an equal chance of being selected. The most commonly used sample is a simple random sample. It requires that every possible sample of the selected size has an equal chance of being used.
A parameter is a characteristic of a population. A statistic is a characteristic of a sample. Inferential statistics enables you to make an educated guess about a population parameter based on a statistic computed from a sample randomly drawn from that population (see Figure 1).
Figure 1.Illustration of the relationship between samples and populations.