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deemphasize or even eliminate tests of significance altogether (see Kline,
2004). We are sympathetic to the arguments that are made on behalf of
this movement because by blindly relying on statistical significance testing
without considering the magnitudes of the effects we are studying, we turn
into automatons rather than researchers. In its defense, we also believe
that there is still a useful purpose to be served by statistical significance
tests with the relatively small sample sizes that we ordinarily see in research
using experimental designs.
4.8 THE LIMITING CASE OF ANOVA: THE
t
Test
A one-way between-subjects ANOVA is designed to compare two or more
levels or groups of the independent variable on a single dependent variable.
Thus, the ANOVA can handle situations in which the independent variable
has two, three, or more levels. Creation of the
t
test predates Fisher's
variance ratio and was specifically designed to compare the means of
exactly two conditions.
4.8.1 A BIT OF HISTORY
The
t
test was developed by William Sealy Gosset, who was interested
in publishing his innovative work. As Salsburg (2001) tells the story, in
1899, Gosset, who had a combined degree in chemistry and mathematics,
was hired by the Guinness Brewing Company primarily for his chem-
istryexpertise.But,asitturnedout,itwashismathskillsthatmadea
bigger difference in brewing beer. One of his first ventures into apply-
ing mathematics to the brewing of beer was estimating yeast amounts in
samples:
When the mash was prepared for fermentation, a carefully measured amount of
yeast was used. Yeast are living organisms, and cultures of yeast were kept alive
and multiplying in jars of fluid before being put into the mash. The workers
had to measure how much yeast was in a given jar in order to determine how
much fluid to use. They drew a sample of the fluid and examined it under a
microscope, counting the number of yeast cells they saw. (Salsburg, 2001, p. 26)
Obviously, there were measurement errors resulting from sampling
the yeast (we would expect different samples to have somewhat different
numbers of yeast cells even if they were relatively evenly distributed in the
mash) as well as from humans counting the yeast cells. Gosset devised a
mathematical model to estimate the error, a critical piece of information
needed by the beer brewers, and he had a desire to publish it. The problem
was that Guinness had a policy forbidding its employees to publish (fearful
that they would reveal corporate secrets). In order to disseminate his work
while at the same time avoiding being fired by the young Lord Guinness,
in 1904 with the help of Karl Pearson he devised the pseudonym “Student”
and published his work in Pearson's
Biometrika
without giving away his
true identity. Gosset continued to publish his mathematical work under his
