In this video I'm gonna show you how to do t-tests in SPSS. A t test is a simple statistical
procedure to determine if two means are significantly different. And it's easy to do in SPSS, but
there are different kinds of t-tests, and they each require the data to be set up slightly
differently in the spreadsheet. So the only trick is knowing how to enter in the data,
and then how to interpret the output. So let's start with a hypothetical example--in my other
videos, I talk about intelligence a lot, so I'm gonna stick with that topic. Let's say
I'm interested in the IQ scores of college students. Specifically, I wanna know whether
college students are more or less intelligent than average. So the first step would be to
collect data. What we can do is get a random sample of college students and administer
an IQ test. Let's pretend we did this with ten college students, and here are their IQ
scores. And I'm gonna go to variable view and just rename this variable IQ scores. so
we know what we're dealing with. Now we're going to perform a test called a one sample
t-test, it compares the mean of your sample data, the mean of all these numbers, against
some hypothesized population mean, to see if they're significantly different. The key
is, you have to pick your hypothesized population mean based on a theory of what you expect
it to be. Now, if I'm trying to figure out if college students are more or less intelligent
than average, I might expect the average intelligence to be around one hundred, because the way
IQ scores are calculated, the average is usually around one hundred. So here's how we do the
one sample t-test. You go to analyze, compare means, and pick one sample t-test. A window
pops up, just like before when we do frequency counts for descriptive stats, here we need
to take our sample data, the IQ scores, and move it over to the box called test variables.
We can do that with the arrow or just dragging it over. Then, we need to type in our hypothesized
population mean in this box called test value. So if we think the population mean is around
one hundred, we type in one hundred. When you're ready, just click OK. The output window
will appear, and you'll see two tables in it. The first table has descriptive stats,
just like if you did analyze, descriptive stats, descriptives. But we didn't, we just
did one sample t test. It just tells us how many scores there are, the mean IQ score,
standard deviation, and something they call the standard error of the mean. The second
table is the one that's gonna have our inferential stats in it. This is where we'll find out
if the mean of our sample is significantly different from one hundred or not. So we have
the t score right here, this tells us kind of in standard error units how many units
away our score is from the average of one hundred. The degrees of freedom, which is
n minus one, number of scores we have minus one, and finally the P value, that corresponds
to this t score at this degrees of freedom. Now typically scientists and researchers use
.05 as the cutoff for statistical significance, where anything .05 or less is said to be statistically
significant. We can see this p value is less than .05, so we can conclude the IQ of our
sample is significantly different from one hundred. Now it's very important to say what
that difference is. We've established there is a significant difference, but we also wanna
say, well, what is that difference? And that's easy to figure out. Just look at your mean.
It's 105, we're comparing it against a test value of 100, if there's a significant difference,
that means the average IQ score of our sample is significantly higher than the average IQ
of the population at large. We can also look at this box over here that says mean difference.
If this difference is positive, that means that are sample is significantly more intelligent
than average. Value is negative, we know the sample is significantly less intelligent than
average. And lucky for the college graduates out there, the number is positive so they're
more intelligent than average. The last cool thing I wanna show you here is this box that
says ninety-five percent confidence interval. Confidence intervals are cool. They tell us
what kind of differences we can expect in a population. So with this example, we got
a sample of ten college graduate IQs. And we used that sample mean to estimate the mean
IQ scores of all college graduates. But we don't really know what the true mean of all
college graduate IQ scores would be. So if we don't know the real IQ of all college graduates,
we don't really know what the difference would be, but this confidence interval gives us
an idea of what that difference might be. It is a range of what kind of difference we'd
expect. So it tells us we are ninety-five percent certain that the average college graduate
IQ is at least 2.12 points above a hundred, and at most 7.88 points above a hundred. Now
we're never one hundred percent certain about something, because any time we deal with samples
there's always the chance the sample might not represent the true population. And the
default setting for the confidence interval is ninety-five percent. But if we wanna change
that, we can do it. Just go back to analyze, and under compare means one sample, click
under Options. We can specify what level of confidence we want to have in our confidence
interval. So let us try doing it for, instead of ninety-five, we're gonna do ninety. Hit
continue and run that again. This part will be the same, but under the ninety percent
confidence interval box, we see that the width is a little bit more narrow. instead of 2.11
to 7.88, now it's 2.66 to 7.33. So in other words, we have a better idea of what the true
difference in the population might be. But the downside of that is that we're only ninety
percent certain instead of ninety-five percent certain. So we have a tighter width, but we're
less confident the true population difference is actually between those two numbers. Likewise,
we can go back and do this again, but instead of for ninety or ninety-five we're gonna do
ninety-nine, run that again. Well, now we're more certain about the lower and the upper
limit, that they really contain the true difference, but if you look, the interval width is much
bigger, now it's .86 to 9.14, so it's telling us with less certainty, well it's giving us
a wider range, there's more variability about what it could be, even though we're more certain
about what that difference could be. So basically it's a tradeoff, you want as narrow an interval
as you can get, but you also want high confidence. And honestly, most people just leave it set
at ninety-five percent. So that's how you do a one sample t-test in SPSS, and how you
get the confidence levels for the difference too. Now it's also possible to do different
types of two sample t-tests, but I'm gonna save that for the next video.