In this video we'll continue with our
discussion of the analysis of the
one-way ANOVA, and now we're going to
focus on post-hoc tests. Recall in our
prioir video that our test was
significant, with a p-value .019, which
indicated that there was a significant
difference somewhere between these three
groups. But we didn't know exactly where
the difference existed at this point. So
we were going to do post-hoc tests to
flush out those differences and see
where in fact they are. Now post-hoc
tests are conducted after the fact. They
are typically only conducted or
interpreted after a significant ANOVA. So we
so We have a significant result, recall,
.019, so that effectively gives us the
green light to go and dive in and try
and find out where the differences lie
between the groups. So post-hoc
tests are used to, as I just said, dive in
and look for the differences between the
groups and, importantly, they test each
possible pair of groups. So they test two
at a time. So, for example, a post-hoc
test will test
none versus low volume, and there will be
another test that tests none vs high
volume, and then there will be a final test
that tests low volume versus high volume. So
it does all possible pairs, two at a time. The
total alpha used for the set of tests is
.05, and that's important to
keep in mind. It's not .05 per test, but
it's .05 in total.
And we're using a test which we selected
in the previous video under the Post-Hoc
button which was called Tukey. We're
going to use Tukey's test, and Tukey's test
does a good job at keeping the whole set
of tests at .05. So the
post-hoc tests for Tukey's test there's
actually two tables that come out;
there's a Post Hoc Tests table, which is
labeled Multiple Comparisons, and then
there's the Homogeneous Subsets table,
which is labeled exam scores. We'll take a
look at each of these in turn. So let's
start with our Multiple Comparisons
result.
Now here the way this is organized is
that we have our pairs organized from
left to right. So, for example, this first
test is none versus low volume, and if we
scroll over, we can zero in on this
column,
these are the p-values. So here the
p-value is .963. And we use the same
decision rule as always, if p is less
than equal to .05, there's a significant
difference between the groups. If p is
greater than .05, there's no
significant difference. So here we can
see that no music and low volume is not
significantly different, since this is
greater than .05. OK our next
result we read here, diagonally, so we
move down diagonally, and this compares
the no volume versus high volume. And as
we read over we can see that this test
is in fact significant at .027.
So there's a significant
difference between no volume and high
volume. Our next result, low volume versus
none, if you look at this low volume
versus none with the p of .963, you know
we've already done this. If you notice it
up here, none versus low volume, low volume
versus none,
these two have the exact same p-values,
this is the same test. And this is one of
the drawbacks of the multiple
comparisons table; it produces actually
the same test twice, for each test, and
we've seen this one right here, so we're
going to ignore this because it tells us
the same thing.
Next we have low volume versus high
volume, and notice that p-value is .049.
So that's very close, but it in fact also is
significant.
So there's a significant difference
between the low volume and the
high-volume groups. As I move down
here, high volume versus none, that test
has already been done here,
notice the same p value .027.
And then high volume low volume, we
just read that one right here, with a p of
.049. So, in summary, the results we have
here are