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t-tests in SPSS.
The t-tests are used to determine if there exists a significant
difference between means. There are traditionally, three types of t-tests.
The seldom used one sample t-test, the dependent samples t-test,
and the independent samples t-test. For the duration of this tutorial, we
will be using
ExampleData001.sav
(1). One sample t-test is used to determine if the sample mean
is different from some constant value; typically assumed to be a population mean.
First, we'll test whether or not our sample mean (in this case age) is
significantly different from zero. Begin by importing the data, then click on
Analyze, Compare Means, One-Sample T test...
Next, highlight the Age variable and use the arrow to move it into the Test
Variable(s): box.
Next, click the OK button to complete the t-test.
The output provides two tables. The first, offers descriptive statistics for
the variable we tested (Age), which includes number of cases/observations, mean,
standard deviation, and standard error. The second table provides the actual
t-test output--where we see that our sample's age (M = 21.04, SD =
1.85) was significantly different from zero, t(53) = 83.440, p <
.001. As you might imagine, this is not terribly useful information. A more
informative test might include testing whether or not our sample is
significantly different from a specified value. SPSS allows us to specify a
value in the One Sample T Test dialog.
Again, click on Analyze, Compare Means, One-Sample T test...
Notice the previous run is still specified (i.e. the Age variable is already
in the Test Variable(s): box.
Next, we want to specify a value, say 20 which might represent the mean of
all undergraduate college students. We simply type the value in the
Test Value: box.
Then click the OK button to complete the t test.
Here, we see that our sample's age (M = 21.04, SD = 1.85) was
significantly different from 20, t(53) = 4.113, p < .001.
(2). Dependent samples t-test is used to determine if the
difference between two related sample means is different from zero. It is
known by many names: dependent samples t test, paired samples t
test, repeated measures t test, etc. SPSS refers to it as the
Paired-Samples T test.
First, click on Analyze, Compare Means, Paired-Samples T test...
Next, select Recalled (Time1) and using the control key and left mouse click
to select Recalled (Time2); which identified the pair of variables you are
testing.
Next, use the arrow button to move the variable into the Paired Variables:
box.
Next, click the OK button to complete the t test.
The three tables produce are fairly self-explanatory. The first provides
descriptive statistics for each variable. The second provides the correlation
between the two variables to verify that the variables are in fact related,
making the dependent t test appropriate. The third table provides the
output for the t test. Here, we can see the difference between Recall at
time 1 (M = 13.35, SD = 5.44) and Recall at time 2 (M =
12.08, SD = 4.96) was significantly different from zero t(53)
= 15.06, p < .001.
(3). Independent samples t-test is used to test whether or not
two independent sample means are significantly different from one another. It is
the most commonly used of the t tests.
Again, begin by clicking on Analyze, Compare Means, Independent-Samples T
test...
Next, select Recalled (Time1) and use the top arrow button to move it to the
Test Variable(s): box. This represents the dependent variable and should be
continuous or nearly continuous. Next, select the Candy Variable and use the
bottom arrow button to move it to the Grouping Variable: box. This represents
our independent or grouping variable.
Next, click on the Define Groups... button. Type a 1 into the Group 1: box
and type a 2 into the Group 2: box. Next, click the Continue button.
You should see the following.
Next, click on the OK button to complete the t test. You should now
see the output resembling the following tables.
As is usually the case, the first table provides descriptive statistics. The
second table provides the results of the t test. Interesting to note is
the Levene's Test for Equality of Variances. This tests the assumption that our
two groups have approximately equal variances; sometimes called the homogeneity
of variance assumption (see
this article
for a discussion). In the current example, the Levene's test indicates we do not
have significantly different variances between our two groups, which is what we
want to see as this supports the assumption. The t test results indicate
that the participants of the Skittles group (M = 9.41, SD = 3.20)
recalled significantly fewer words than did the participants of the no candy
group (M = 17.30, SD = 4.20), t(52) = -7.76, p <
.001.
(4) Effect Size
It is no longer acceptable to simply report the statistics and their
associated p values for inferential procedures. An effect size should
also be reported with every inferential analysis. The appropriate effect size
metric for a t test is d (Cohen,
1992), which involves a relatively simple calculation and provides a
standardized estimate of the difference between two groups. Unfortunately, SPSS
does not provide any way of obtaining Cohen's d. The formulas are
available in both the article provided and at
Wikipedia for calculating
Cohen's d for each type of t test reviewed here.
Reference
Cohen, J. (1992). A power primer. Psychological Bulletin, 112, 115 -
159. doi: 10.1037/0033-2909.112.1.155
(5). Graphing
We'll use a bar chart because we are dealing with a categorical variable
whose effect is shown on a continuous variable. One could also use other types
of graphical representations. To graph the Independent Samples T test effect we
have discovered, simple click on Graphs, Legacy Dialogs, Bar...
Next, click on the Define button (the defaults Simple & Summaries for groups
of cases are appropriate for this example). Next, click
on the circle next to Other statistic (e.g., mean).
Next, highlight the variable Recalled (Time1) [Recall1] and use the top arrow
button to move it to the Variable: box in the Bars Represent area. Then,
highligh the variable Candy Consumed [Candy] and use the second arrow from the
top to move it to the Category Axis: box. Next, click the OK button.
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