Inferential Statistics


Learning Objectives

  1. Distinguish between a sample and a population
  2. Define inferential statistics
  3. Describe the various types of sampling and the implications of using each

With inferential statistics, we generally take a sample, or a small subset of a larger set of data, and we use this sample to draw inferences about the population as a whole.

As you might be able to imagine, it is very easy for a sample to be biased. Thus, there are strategies that researchers adopt in an attempt to eliminate or decrease the bias in their sample. One of these strategies is the use of simple random sampling. Simple random sampling occurs when every member of the population has an equal chance of being selected into the sample. In addition, the selection of one member is independent from the selection of another member.

Sometimes, however, it is simply not possible or feasible to take a simple random sampling. For instance, consider the fact that both Dallas and Houston are vying to be hosts of the 2012 Olympics. And consider that you are hired to assess whether Texans, as a whole, would prefer the Olympics to be in Dallas or Houston. Because you have already learned the difficulty of getting every single Texan's opinion, you know you must get a sample and you want to use a simple random sampling. However, even this may be very difficult. Consider, for instance, how will you get a hold of those individuals who don’t vote, who don’t have a phone, and show address has changed? What do you do with those individuals in the sample how happened to move from Texas to California? What do you do about the fact that since the beginning of the study, an additional 4,212 people moved to the state of Texas? As you can see, it is sometimes very difficult to develop a truly random procedure.

Recall that the definition of a random sample is a sample in which every member of the population has an equal chance of being selected. This means that the sampling procedure rather than the results of the sampling procedure define what it means for a sample to be random. Random samples, especially if the sample size is small, are not necessarily representative of the entire population. Inferential statistics use mathematical models that take sample size into account when generalizing from a sample to a population.

Random Assignment

In experimental research, populations are often hypothetical. For example, in an experiment comparing the effectiveness of a new anti-depressant drug with a placebo, there is no actual population of individuals taking the drug. In this case, a specified population of people with some degree of depression is defined and a random sample is taken from this population. The sample is then randomly divided into two groups; one group is assigned to the treatment condition (drug) and the other group is assigned to the control condition (placebo). This random division of the sample into two groups is called random assignment.