here we want to move volume to Break
Variable(s) and then exam scores to Summary
of Variable(s). So go ahead and click OK.
And then we'll go back to our Data
Editor window. And now you can see here
we have the mean, 84.9, repeated over and
over for each value in the first group.
So the mean of group 1 or no volume is
84.9. And then we have the mean for the
second group, or high volume, of 77.5, and
SPSS repeats that for each observation,
which can come in quite handy. So now I
want to find the difference score, or in
other words, take the score for a person
and subtract the mean from it, and find
that difference. I'm going to have that
put in this column here. So to do that we
go to Transform and then Compute. And
then here I'm going to make a new
variable which I'll just shorthand here
and call Diff, for difference. And that
will be equal to exam score, this value
here, so double-click exam score, SPSS
puts it over here, type in a minus, and
then we're going to subtract the mean,
which is given as exam scores mean. So go ahead and
double-click on that. You should
see here exam scores minus exam scores
mean. And I'll go ahead and add some
spaces there, so you can see that minus
sign a little better.
Go ahead and click OK. Let's go back to
our Data Editor.
And now in our difference column, or Diff,
we can see the difference score, where we
have 84-84.9 is -.9. 80-84
.9 is -4.9, and so on.
If we sum up these values, they will
equal 0.
To back up for a moment, while this is a
measure of variability, notice this tells
us how far a score varies from the mean
of 84.9 This value varies from the mean
of 84.9 by 4.9 points, and it
happens to be below the mean because
it's negative. 80 is 4.9 points below
this value. And that's all this
difference column reflects.
But because these add up to 0 we need to
do something to get rid of these
negative values. And what Levene's test
does is, it takes the absolute value of
these values. In other words, it makes it
so that every value is positive, and then it
works on those values. So let's go ahead
and calculate an absolute value of each
of these values first. And we'll do that
by going to Transform, Compute Variable,
and then here let's click, so it
clears everything out. And then I want to make
a new variable which are short-handed as
Abs, for absolute value, and then Diff. So
the absolute value of the difference
score. And the way I can do that is, I'm
going to use the absolute value function
in SPSS. If I click under Function group
on Arithmetic, double-click on that, and
then select Abs, for absolute value. Notice it
says here,
returns the absolute value of numeric
expression, which is whatever's in the
parentheses here, which must be numeric.
OK so let's go ahead and move our
variable here, Diff.
Notice it's selected here, so
double-click Diff, and it'll put that in
there. So we're getting the absolute
value of the difference scores, or the
absolute value of these values here in
this column. So that looks good.
Go ahead and click OK. Go back to our
Data Editor. Notice here now, you should
see, that we just have positive values. In
other words, the negative values are now
gone and they're replaced with positive
values, or we took the absolute value of
all those scores.
Now Levene's test works on these values.
Levene's test performs an ANOVA on the
absolute value of the difference of the
scores from their respective group mean.
Now that's quite a mouthful, but that's
exactly what it does, and that's what we
just did ourselves. We found the absolute
value of the difference scores of each
score how far it is from its respective
group mean.
OK that's what this column is. Now the
only thing we haven't done is run the
ANOVA on this yet. So let's go ahead and
do that. We'll do ANOVA on these values,
this will be our dependent variable. OK so we
go to Analyze, Compare Means, and then
One-Way ANOVA. And then here we're going
to kick-out exam scores, we don't want
exam scores anymore,
instead we want absolute value
difference. So we'll move that over and
then click OK. And then here I'm going to
delete just a few things here, so we can
line up these two tables and take a look
at them.
Notice the two tables I have selected
here. This was the homogeneity of
variance table from our earlier ANOVA, and
then here's our ANOVA on the absolute
value of the difference scores. And
notice our F here .078 and the p-value
.783. Notice how these two values match up
exactly with the values in our Test of
Homogeneity of Variances table. We
have our Levene of .078, you can see that
down here, and we have a p-value of
.783, which you can also see
down here in the ANOVA table, and the
same degrees of freedom of 1 and 18
which we can see in our ANOVA table.
So this demonstrates that the Levene
test is in fact an ANOVA,
or analysis of variance, on the absolute
value of the difference scores, in other
words, the difference between each score
and its respective group mean.
So that's it for Levene's test. Hopefully
that gives you a little bit of a better
idea of what it is that Levene's test is
assessing, when it's run in either the
t-test or the ANOVA. This concludes the
video on the Levene's test of equality of
variances in SPSS. Thanks for watching.