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Chapter 5
Two-Group t-Test of the Difference
of the Means for Independent Groups
Up until now in this topic, you have been dealing with the situation in which you
have had only one group of people, plants, or animals in your research study and
only one measurement ‘‘number’’ on each of these people, plants, or animals. We
will now change gears and deal with the situation in which you are measuring two
groups instead of only one group.
Whenever you have two completely different groups of people (i.e., no one
person is in both groups, but every person is measured on only one variable to
produce one ‘‘number’’ for each person), we say that the two groups are ‘‘inde-
pendent of one another.’’ This chapter deals with just that situation and that is why
it is called the two-group t-test for independent groups.
The two assumptions underlying the two-group t-test are the following
(Zikmund and Babin 2010 ): (1) both groups are sampled from a normal
population, and (2) the variances of the two populations are approximately equal. Note
that the standard deviation is merely the square root of the variance. (There are
different formulas to use when each person is measured twice to create two groups
of data, and this situation is called ‘‘dependent,’’ but those formulas are beyond the
scope of this topic). This topic only deals with two groups that are independent of
one another so that no person is in both groups of data.
When you are testing for the difference between the means for two groups, it is
important to remember that there are two different formulas that you need to use
depending on the sample sizes of the two groups:
1. Use Formula #1 in this chapter when both of the groups have a sample size
greater than 30, and
2. Use Formula #2 in this chapter when either one group, or both groups, have a
sample size less than 30.
We will illustrate both of these situations in this chapter.
But, ﬁrst, we need to understand the steps involved in hypothesis-testing when
two groups are involved before we dive into the formulas for this test.
T. J. Quirk et al., Excel 2010 for Biological and Life Sciences Statistics,
DOI: 10.1007/978-1-4614-5779-4_5,
Springer Science+Business Media New York 2013
83
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