Independent and Dependent Variables in Statistics

Independent and/or dependent variables occur in almost any situation in which statistics is used.

It is important that any professional, whose field requires the use of statistics, understands the difference between independent and dependent statistical variables. Being able to distinguish between independent and dependent variables will help the professional determine which statistical tests and equations to use as well as to facilitate the interpretation of any statistical analysis.

Independent Statistical Variables

An independent statistical variable is a quantity which is able to be varied or manipulated within the context of some given situation. The previous sentence may seem to be highly technical so let’s clarify it with the use of a few examples.

The first two examples come from the sciences of psychology and medicine while the third example comes from business. These three diverse subjects have been chosen in order to illustrate the range of application of the concepts found within statistics.

The first example consists of a psychologist who wishes to determine whether or not running for 30 minutes can help to improve test scores. To do this, but psychologist performs an experiment in which participants are separated into two groups.

The first group runs for 30 minutes before performing a test while the second group relaxes for 30 minutes before performing the exact same test.

This experiment examines both the case in which running is performed for 30 minutes before taking the test and the case in which one relaxes for 30 minutes before taking the test.

Therefore, the independent variable can be identified with whether one runs or relaxes for 30 minutes before taking the test. Furthermore, the independent variable can take on either of two values within this particular example, the first value being that the individual runs for 30 minutes before taking the test while the second value is that the individual relaxes before taking the test.

The second example comes from business. In this example, a researcher wants to know if sending a thank you letter can increase repeat business. To study this, the researcher sends a thank you letter to 50 customers and does not send a thank you letter to 50 other customers.

The statistical variable which is being varied within this study is whether or not a customer receives a thank you letter. Therefore, the independent variable is whether or not a customer receives a thank you letter. As with the first example, the independent variable can take on one of two possible values with the first value being that a given customer receives a thank you letter and the second value being that a given customer does not receive a thank you letter.

It is important to mention that while each of the independent variables took on two values, in general, independent variables can take on any number of values.

Dependent Statistical Variables

A dependent statistical variable is a quantity which is measured. Each of the examples of the previous section contains a single dependent variable.

Recall that the first example consisted of a psychologist who wanted to determine whether or not running could increase test scores. The quantity which is being measured is the test score of each participant.

Therefore, the dependent variable is the test score of each participant.

The second example of the previous section consisted of a researcher who wanted to find whether or not if sending thank you letters is able to increase repeat business.

Suppose that the amount of repeat business is determined by how much products or services are reordered by a customer after 30 days of a purchase. Then the dependent variable will be equal to the amount of products or services reordered by a customer after 30 days of a purchase.

Conclusion

Understanding the difference between independent and dependent statistical variables is important if we are to perform a statistical analysis that will help us to uncover relationships between the parameters relevant to a phenomenon, behavior or practice.