Welcome to the fifth video in SPSS for Beginners from RStats Institute at
Missouri State University. Earlier, we learned how to calculate means using
SPSS, so now I'm going to show you how we test whether two means are different
(or not) using a procedure called the one sample t-test. T tests are easy to do
in SPSS. In the next three videos, we will learn about three kinds of T tests. Each
of them will use the data set that we created in the first video. I'm
interested in the variable Height. Specifically, I want to know if my
participants are taller or shorter than the national average.
Perhaps we sampled these people from a certain country and we want to know how
they compare to the average American. Or perhaps they have a certain disorder and
I want to know how they compare to the typical average healthy person. Or
perhaps these are children who grew up eating a certain diet and I want to know
if that diet affected their height compared to an average child. So what I
have is one group of people whom I have measured one time. I want SPSS to
calculate the mean from my sample and then compare that sample mean to another
known mean. And to do this, I'm going to use a one sample t-test.
Go to Analyze -> Compare Means -> One Sample t-Test. A window pops up just like we
have seen before. We will move our variable Height into the Test Variables
box. We can do that with the arrow or just by dragging it over. And then we
need to set our hypothesized population mean in this box - labeled Test Value.
So imagine that we went to the scientific literature and we read that other people,
similar to this sample, have an average height of 65 inches tall.
I want SPSS to calculate this sample mean and then compare it to the known
value of 65. So, click OK. The output window will pop up and you will see two
tables. The first table contains our descriptive statistics, just like we've
calculated before. We see the mean, standard deviation, and something called
the standard error of the mean. The second table contains our inferential
statistics, and this is where we find out if the mean of our sample is
significantly different from 65, or not. We have the t-score right here, the
degrees of freedom (which is n - 1) the number of scores minus 1, and finally
the p-value that corresponds to this t-score at this degrees of freedom. In the
box "Sig. (2-tailed)." There are three ways that we can determine if one mean
is statistically significantly different from another mean. The first is by
looking at the t-value. We would go to a table called "Students t-Table" and look
up a Critical Value. If the T value is larger than the
critical value from that table, then the means are different. A second way is to
look at the p-value. Typically, scientists and researchers use p < .05 as
the cutoff for statistical significance, where any values .05 or
less are said to be "statistically significant." A third way of determining
significance is to look at the confidence interval. We are testing a
hypothesis that the mean difference was 0. So if the 95% confidence interval
includes 0, then the means are NOT different. So, I looked up the critical
value on Students t-Table and I found that for a test with 9 degrees of
freedom, the critical value is 2.262. This t value is smaller than
2.262. I can see that the p-value is .318, which
is larger than .05. And finally, I can see that the lower
confidence interval is negative but the upper value is positive, so this
confidence interval crosses zero. These three findings all tell us the
same thing: the mean of our sample 65.8 is NOT different than
the national average of 65. Our sample was pretty much the same height as our
comparison group. And that is how you do a one sample t-test in SPSS. When you are
ready to do a real one sample t-test, check out these other videos from
RStats Institute that will teach you more about statistical theory, setting up the
test, interpreting the results, and writing up your findings in APA style.