Descriptive versus Inferential Statistical Analysis

To understand the difference between descriptive and inferential statistics, you must first understand the difference between populations and samples. A population is the entire collection of a carefully defined set of people, objects, or events. For example, if the insurance company in question employed 10,000 insurance agents in the European Union, then those 10,000 agents would constitute the population of agents hired by that company. A sample, on the other hand, is a subset of the people, objects, or events selected from a population. For example, the 100 agents used in the experiment described earlier constitute a sample.

Descriptive Analyses

A parameter is a descriptive characteristic of a population. For example, if you assessed the average amount of insurance sold by all 10,000 agents in this company, the resulting average would be a parameter. To obtain this average, of course, you would first need to tabulate the amount of insurance sold by each and every agent. In calculating this average, you are engaging in descriptive analysis. Descriptive analyses organize, summarize, and identify major characteristics of the population.

Most people think of populations as being very large groups, such as all of the people in the United Kingdom. However, a group does not have to be large to be a population, it only has to be the entire collection of the people or things being studied. For example, a teacher can define all twelfth-grade students in a single school as a population and then calculate the average score of these students on a measure of class satisfaction. The resulting average would be a population parameter.

Inferential Analyses

A statistic, on the other hand, is a numerical value that is computed from a sample and either describes some characteristic of that sample such as the average value, or is used to make inferences about the population from which the sample is drawn. For example, if you were to compute the average amount of insurance sold by your sample of 100 agents, that average would be a statistic because it summarizes a specific characteristic of the sample. Remember that the word “statistic” is generally associated with samples while “parameter” is generally associated with populations.

In contrast to descriptive analyses, inferential statistics involve information from a sample to make inferences, or estimates, about the population (i.e., infer from the sample to the larger population). For example, assume that you need to know how much insurance is sold by the average agent in the company. It might not be possible to obtain the necessary information from all 10,000 agents and then determine the average. An alternative would be to draw a random (and ideally representative) sample of 100 agents and determine the average amount sold by this subset. A random sample is a subset of the population in which each member of that population has an equal chance of selection. If this group of 100 sold an average of $179,322 worth of policies last year, then your best guess of the amount of insurance sold by all 10,000 agents would likewise be $179,322 on average. Here, you have used characteristics of the sample to make inferences about characteristics of the population. This is the real value of inferential statistical procedures; they allow you to examine information obtained from a relatively small sample and then make inferences about the overall population. For example, pollsters conduct telephone surveys to ascertain the voting preferences of Canadians leading up to, and between, federal elections. From randomly selected samples of approximately 1,200 participants, these pollsters can extrapolate their findings to the population of 20 million eligible voters with considerable accuracy (i.e., within relatively narrow limits).