1. The One-Sample T-Test

 

A brief history of the t-test

 

Just past the turn of the nineteenth century, a major development in science was fermenting at Guinness Brewery. William Gosset, a brewmaster, had invented a new method for determining how large a sample of persons should be used in the taste-testing of beer. The result of this finding revolutionized science, and – presumably - beer. In 1908 Gosset published his findings in Biometrika under the pseudonym “student.” This is why the t-test is often called the “student’s t.”

 

Here’s where some folklore begins. Two stories circulate regarding the reason why Gosset failed to use his own name in publishing his results. First, Guinness may have wanted to keep their use of the “t-test” secret. By keeping Gosset out of the limelight, they could also protect their secret process from rival brewers. The second story claims that Gosset was embarrassed to have his name associated with either: a) the liquor industry, or b) mathematics. But seriously, how could that be?

 

I think the most interesting part of this story can be illustrated by a quote from Homer Simpson, “Beer is the cause of - and solution to - all of life's problems.” If you don’t get that, don’t worry. You soon will.

 

When to use the one-sample t-test

 

One of the most difficult aspects of statistics is determining which procedure to use in what situation. Mostly this is a matter of practice. There are many different rules of thumb which may be of some help. In practice, however, the more you understand the meaning behind each of the techniques, the more the choice will become obvious.

 

The next example problem illustrates the calculation of the one-sample t-test. This test is used to compare a list of values to a set standard. What is this standard? The standard is any number we choose. As illustrated below, the standard is usually chosen for its theoretical or practical importance.