E. The T-Test

Introduction

How are outcomes different for different groups? It's a question of central concern to the social sciences, for outcomes vary by a number of characteristics: where we live, how far we went in school, what kind of job we have, and so on.

One goal of social science research is to accurately measure the social world, to document the levels of different features of society.

So we are concerned with the measurement of phenomena and strive to specify the level of difference in voting behavior, household income, or feelings of self-efficacy. However, we often want to use these measurements in evaluating specific hypotheses about these differences.

In this module, you will learn to use a statistical tool to evaluate hypotheses about group-level differences in outcomes: the t-test. Specifically, you will learn to use two different applications of the t-test in evaluating two kinds of hypotheses:

  • The one-sample t-test, in which the level of outcome for a group is compared to a known standard.
  • The two-sample t-test, where the outcome levels of two groups are compared to each other.

History and Main Ideas

The t-test was developed by W. S. Gossett, a statistician employed at the Guiness brewery. However, because the brewery did not allow employees to publish their research, Gossett's work on the t-test appears under the name "Student" (and the t-test is sometimes referred to as "Student's t-test.") Gossett was a chemist and was responsible for developing procedures for ensuring the similarity of batches of Guiness. The t-test was developed as a way of measuring how closely the yeast content of a particular batch of beer corresponded to the brewery's standard.

But the t-test has applications well beyond the realm of quality beer. Applied to the social world, the same kinds of questions addressed by the t-test in the brewery (how different is a particular batch of beer from the desired standard?) can be useful in the social world. How different are the SAT scores of political science undergraduates of a particular university from the SAT scores of the average SAT scores of the university's undergraduate population?

And the same statistical methodology that compares a particular batch of beer to a standard can be used to compare how different any two batches are from each other. The test can be used to compare the yeast content of two kegs of beer brewed at separate times. Extending this into the realm of social phenomena, we can use this methodology to address questions such as whether SAT preparation courses improve test scores or whether African Americans continue to face discrimination in the housing market.

One of the advantages of the t-test is that it can be applied to a relatively small number of cases. It was specifically designed to evaluate statistical differences for samples of 30 or less.