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Matched pairs (“paired” or “dependent” samples) t-tests in SPSS
Bro. David E. Brown, BYU–Idaho Dept. of Mathematics
February 2, 2012
Note: SPSS always uses t-scores for two-sample tests of means, never z-scores. Note: The
SPSS Paired Differences tool tests the null hypothesis that the mean of the population of differences is
0. In symbols, this is H0 : µd = 0 (as opposed to H0 : µd = 32 or H0 : µd = −6 or something).
1. Start SPSS and enter your data or open your data file. There must be two measurements for each
subject.1 This means having two columns of measurements, so that each subject has their two measurements in different columns of the same row.2
2. Make any necessary adjustments in the Variable View. Pay particular attention to the Measurement
levels of your variables. After all, if the data aren’t scale, we shouldn’t be using them in a t-test.
3. In the Analyze menu, click Compare Means. A submenu appears.
4. In the submenu, click Paired-Samples T Test... The Paired-Samples T Test dialog will appear.
5. Because your measurements are paired, you have two columns of measurements. Put the name of one
of them in the Paired Variables: box, by selecting the column’s name and clicking the arrow. SPSS
will put this name in the Variable 1 column.
6. Put the name of the other column of measurements in the Paired Variables: box, by selecting the
column’s name and clicking the arrow. SPSS will put this name in the Variable 2 column. Note: If
the OK button does not become available at this point, make sure that there is a variable
name in the Variable 1 column, a variable name in the Variable 2 column, and no other
variable names in the Paired Variables: box.
7. SPSS will give you a confidence interval for the mean of the differences, whether you want one or not.
The default confidence level is 95%. If you’d like some other confidence level, then. . .
• . . . Click Options. The Paired-Samples T Test:
Options dialog will appear.
• You will see an entry for Confidence Interval Percentage and a box with a number in it,
followed by a percent sign. The number in the box is the confidence level for your confidence
interval. The default value is 95, for 95% confidence. If you want a different confidence level, type
it in the box, as a percentage (not as a decimal number).
• Click Continue. SPSS will return you to the One-Sample T Test dialog.
8. Click OK. The result of the hypothesis test will appear in the the PASW Statistics Viewer output
window, as follows:
• First, there is a Paired Samples Correlations table. (My 200-level Stats classes do not use
this table. Students in these classes would do well to delete this table from their SPSS output.)
It tells you:
1 Or,
2 In
for each “experimental unit,” if you’ve been taught this term.
other words, the measurements are not “stacked” in one column.
1
– The names of the variables it used for the test
– N, which is the number of valid data SPSS used in its calculations. It’s supposed to be equal
to n, the number of data in your data set. Always check this number, to ensure all
your data were used.
– Correlation, which is the “linear correlation coefficient” you may have heard about. We’re
not using it at the present time.
– Sig., which is the 2-tailed P -value of an hypothesis test we’re not using. (The P-value we
need is in the next table.)
• Next is the Paired Samples Test table. It gives you:
– Mean, which is the mean of the differences between the values of the two variables you’re using
– Std. Deviation, which is the standard deviation of the sample of differences
– Std. Error Mean, which is an estimate of the standard deviation of the population of sample
means of differences
– 95% Confidence Interval of the Difference. This is actually a 95% confidence interval
for the mean of the differences (which we call µd , in my classes). The lower bound of the
confidence interval can be found beneath the word under, and the upper bound is beneath the
word Upper. Note: If you chose some other confidence level than 95%, the Paired Samples
Test table will show the percentage you chose, rather than 95%.
– t, which is the t-score (or, test statistic) of your paired-samples t-test.
– df, the number of degrees of freedom used for your t-test. (Recall that df = n − 1 for this
test, even though you have two measurements for each of your experimental units.)
– Sig. (2-tailed), which is the P -value of the two-tailed version of your hypothesis test.
So, if your alternative hypothesis was Ha : µd 6= µ0 , this is the P -value you need. If you have
a one-tailed test (that is, if your alternative hypothesis is H0 : µd < µ0 or H0 : µd > µ0 ),
you’ll need to divide Sig. (2-tailed) by 2.
As always, if you have questions, please ask them!
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