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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 (or objects, plants, or animals) in your research
study and one measurement “number” on each of these. This chapter asks you to
change gears and deal with the situation in which you are measuring two groups of
instead of only one group.
The nine steps for hypothesis-testing using the two-group t-test are presented,
including the decision rule for either accepting or rejecting the null hypothesis for
your data, and writing both the result and conclusion of your statistical test.
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 “indepen-
dent 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 book 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.
T.J. Quirk et al., Excel 2007 for Biological and Life Sciences Statistics ,
DOI 10.1007/978-1-4614-6003-9_5, # Springer Science+Business Media New York 2013
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