Transcript Lesson 2 in SPSS - West Virginia University

THE DATASET
Let’s use our example dataset
from the Lesson 9 PowerPoints.
In this dataset, we have two
variables—grade and score.
There are three levels of the
treatment grade—3rd, 4th, and
5th.
There are five scores in each
grade.
THE SET-UP
The first decision we have to make is whether we have an independent
samples or a related samples experiment. Because there has been no
matching (we didn’t pair up a 3rd grader with a similar 4th and 5th
grader) and we haven’t repeatedly measured the same child as they
progressed through the three grades, we need to do an independent
measures F-test.
THE SET-UP
Do we want to use a one-tailed or a two-tailed test? UHHHHTT. Trick
question. An ANOVA ONLY uses a one-tailed test to determine if the
obtained F-statistic is greater than the critical F-value from the table.
Let’s state our hypotheses:
 Null hypothesis H0: m1 = m2 = m3.
 Alternative hypothesis Ha: At least one mean is different.
SELECTING THE ANALYSIS
From the SPSS menu
bar, choose
Analyze
Compare means
One-Way ANOVA
SELECT THE VARIABLES
The dependent
variable goes in the
Dependent List box. In
this case, we were
measuring the variable
Score.
The independent
variable goes in the
Factor box. Here, it’s
the Grade level.
Next, let’s click on Options
and see what else we might
want to include in our output.
GROUPING VARIABLE
Clicking on the Descriptive
box will include a variety of
descriptive statistics such
as the means and standard
deviations of each
treatment.
The Homogeneity of
variance test will conduct a
Levene’s test.
Then, click on the Continue
button.
MORE TO DO
After having picked our
options, we are returned to our
One-Way ANOVA window.
Since there are three
treatment groups, if our F-test
proves to be significant we will
want to have a post hoc test
performed.
CHOOSING POST HOC TESTS
SPSS offers many
choices for post hoc
tests. Let’s choose
three.
POST HOC TEST INFO
Here’s a little info on the post hoc tests we’ve chosen.
 You learned how to do the Tukey’s test by hand. This is the most
liberal of the three tests picked. That means that smaller
differences between treatment means will be significant than in
some other post hoc tests.
 The Bonferroni’s is a nice test. Not too liberal; not too conservative.
And it takes into account the number of comparisons to be made.
It can be used under a wide variety of circumstances.
 The Scheffe’s test is the most conservative. It is possible that a
Scheffe’s post hoc will indicate no significant differences between
pairs of means when the F-test was significant.
READY, SET,…
Click on Continue to
go back to the main
ANOVA window.
GO!
Now we can click on OK to
run the analyses.
THE OUTPUT
Descriptives
Score
95% C onfidence Interval for
Mean
N
Mean
Std. Deviation
Std. Error
Lower Bound
Upper Bound
Minimum
Maximum
3
5
4.00
1.871
.837
1.68
6.32
2
4
5
6.00
2.121
.949
3.37
8.63
4
9
5
5
8.00
1.581
.707
6.04
9.96
6
10
15
6.00
2.420
.625
4.66
7.34
2
10
Total
The first part of the output gives
us basic statistics about our three
grades. Just as we saw in our
hand calculations, the mean for
the 3rd graders was 4, the mean
for the 4th graders was 6, and the
mean for the 5th graders was 8.
7
• We also can see the standard deviation for
each group.
• Since one of the assumptions of an ANOVA is
that the variances for the groups are about
equal, we’ll need to do a test to be sure this is
the case.
•SPSS also gives us a 95% confidence interval
for the mean. But we should use this only if
we find a significant difference in the means.
THE OUTPUT
And here’s the Levene’s test for equal
variances. You might remember from the
t-test that equal variances is an
assumption of testing differences in
means.
Test of Homogeneity of Variances
Score
Levene
Statistic
.216
df1
df2
2
Sig.
12
.809
• The null hypothesis says that the group variances are NOT significantly different
from each other.
•
As you can see here, the significance on this test is .809, which is way bigger
than .05, so we fail to reject the null hypothesis and conclude that the group
variances are not significantly different. And that’s a GOOD thing!
THE OUTPUT
And here are the results from our ANOVA. Notice that the source table looks
exactly as it did when we calculated it by hand.
Notice that there are 2 degrees of freedom Between groups and 12 Within
groups. We can see that SPSS has calculated both the Sum of Squares and
the Mean Squares.
Our obtained F-value is 5.714. Wow, that’s exactly what we got when we did
it by hand! SPSS gives us a specific significance level of .018, which is
smaller than .05. Therefore, we can immediately tell we have a significant Ftest without having to look anything up in the table.
ANOVA
Score
Sum of
Squares
df
Mean Square
Betw een Groups
40.000
2
20.000
Within Groups
42.000
12
3.500
Total
82.000
14
F
5.714
Sig.
.018
THE OUTPUT
Now that we know there are significant differences between at least one pair of
means, we look at the post hoc table to see where those differences are. Let’s start
out looking at the results for the Tukey’s.
Look at the top tier of the table where it says Tukey HSD 3
4. The value of
-2.000 tells you that the means for the 3rd graders and the 4th graders were
different by 2.000 (6 – 4). The significance level there is .249, which is not < .05 so
these two means are not significantly different.
Multiple Comparisons
Dependent Variable: Score
Tukey HSD
(I) Grade
3
4
5
Scheffe
3
4
(J) Grade
4
Mean
Difference
(I-J)
95% C onfidence Interval
Std. Error
Sig.
Lower Bound
Upper Bound
-2.000
1.183
.249
-5.16
1.16
5
-4.000*
1.183
.014
-7.16
-.84
3
2.000
1.183
.249
-1.16
5.16
5
-2.000
1.183
.249
-5.16
1.16
3
4.000*
1.183
.014
.84
7.16
4
2.000
1.183
.249
-1.16
5.16
4
-2.000
1.183
.278
-5.30
1.30
5
-4.000*
1.183
.018
-7.30
-.70
3
2.000
1.183
.278
-1.30
5.30
THE OUTPUT
But the difference between 3rd graders and 5th graders was -4.000. See the *? That
tells you that SPSS has identified this as a significant difference. The specific
significance level here is .014.
This is the only significant difference found between pairs of treatment group
means. Therefore, the 3rd graders scored significantly lower than the 5th graders,
but the 3rd graders were not significantly different from the 4th graders and the 4th
graders were not significantly different from the 5th graders.
Multiple Comparisons
Dependent Variable: Score
Tukey HSD
(I) Grade
3
4
5
Scheffe
3
4
(J) Grade
4
Mean
Difference
(I-J)
95% C onfidence Interval
Std. Error
Sig.
Lower Bound
Upper Bound
-2.000
1.183
.249
-5.16
1.16
5
-4.000*
1.183
.014
-7.16
-.84
3
2.000
1.183
.249
-1.16
5.16
5
-2.000
1.183
.249
-5.16
1.16
3
4.000*
1.183
.014
.84
7.16
4
2.000
1.183
.249
-1.16
5.16
4
-2.000
1.183
.278
-5.30
1.30
5
-4.000*
1.183
.018
-7.30
-.70
3
2.000
1.183
.278
-1.30
5.30
5
-2.000
1.183
.278
-5.30
1.30
THE OUTPUT
Next, let’s look at the Bonferroni’s.
The test results are essentially the same.
Multiple Comparisons
th graders.
That is,Dependent
3rd graders
Variable: Score are significantly different from 5
Mean level is slightly higher than in the Tukey’s.
But notice that the significance
95% C onfidence Interval
Difference
This is the sign(I) Grade
that the
Bonferroni’s
more
conservative
test than
(J) Grade
(I-J)
Std.is
Errora slightly
Sig.
Lower Bound
Upper Bound
Tukey HSD
3
4
-2.000
1.183
.249
-5.16
1.16
the Tukey’s. Mean’s 5have to be-4.000*
just a 1.183
little bit.014more different
to-.84reach the
-7.16
4
3
2.000
1.183
.249
-1.16
5.16
same significance
level
in a Bonferroni’s
than
in
a
Tukeys.
5
-2.000
1.183
.249
-5.16
1.16
5
Scheffe
3
Dependent Variable: Score
4
3
4.000*
1.183
.014
.84
7.16
4
2.000
1.183
.249
-1.16
5.16
1.30
4
Multiple
-2.000 Comparisons
1.183
.278
-5.30
5
-4.000*
1.183
.018
-7.30
-.70
3
2.000
1.183
.278
-1.30
5.30
1.183
.278
-5.30
1.30
1.183
.018
5
Tukey
HSD
Bonferroni
5
3
(I) Grade
3
4 Grade
(J)
4
4
5
-2.000
Mean
4.000*
Difference
(I-J)2.000
1.183
Std. Error
Sig..278
-1.30
Lower Bound
5.30
Upper Bound
-2.000
1.183
.249
.350
-5.16
-5.29
1.16
1.29
5
-4.000*
1.183
.014
.016
-7.16
-7.29
-.84
-.71
3
2.000
1.183
.249
.350
-1.16
-1.29
5.16
5.29
5
-2.000
1.183
.249
.350
-5.16
-5.29
1.16
1.29
3
4.000*
1.183
.014
.016
.84
.71
7.16
7.29
4
2.000
1.183
.249
.350
-1.16
-1.29
5.16
5.29
1.183
.278
-5.30
1.30
1.183
.018
-7.30
-.70
Scheffe
3
-2.000
*. The mean difference
is s 4
ignificant at the .05 level.
5
-4.000*
4
5
Bonferroni
3
4
.70
95% C onfidence
Interval 7.30
3
2.000
1.183
.278
-1.30
5.30
5
-2.000
1.183
.278
-5.30
1.30
3
4.000*
1.183
.018
.70
7.30
4
2.000
1.183
.278
-1.30
5.30
4
-2.000
1.183
.350
-5.29
1.29
5
-4.000*
1.183
.016
-7.29
-.71
3
2.000
1.183
.350
-1.29
5.29
The Output
•
•
Finally, let’s look at the Scheffe’s. Again, the test results are essentially the
same. That is, 3rd graders are significantly different from 5th graders.
But once again, notice that the significance level is slightly higher in the
Scheffe’s than in the Bonferroni’s, and a bit higher than in theTukey’s. As I
Multiple Comparisons
said in the previous slide, is the
sign that the Scheffe’s is a slightly more
Dependent Variable: Score
conservative test than the Bonferroni’s, and therefore, a bit more
Mean
considerative than the Tukey’s.
95% C onfidence Interval
Difference
Tukey HSD
(I) Grade
3
Dependent Variable: Score
4
(J) Grade
4
-.84
3
2.000
1.183
.249
-1.16
5.16
1.183
.249
-5.16
1.16
1.183
.014
4 Grade
(J)
4
4
5
1.16
-7.16
(I) Grade
3
3
Upper Bound
.014
-2.000
Mean
4.000*
Difference
(I-J)2.000
.84
95% C onfidence
Interval 7.16
1.183
Std. Error
Sig..249
-1.16
Lower Bound
5.16
Upper Bound
-2.000
1.183
.249
.278
-5.16
-5.30
1.16
1.30
-4.000*
1.183
.014
.018
-7.16
-7.30
-.84
-.70
3
2.000
1.183
.249
.278
-1.16
-1.30
5.16
5.30
5
-2.000
1.183
.249
.278
-5.16
-5.30
1.16
1.30
4.000*
1.183
.014
.018
.84
.70
7.16
7.30
4
2.000
1.183
.249
.278
-1.16
-1.30
5.16
5.30
4
-2.000
1.183
.278
.350
-5.30
-5.29
1.30
1.29
5
-4.000*
1.183
.018
.016
-7.30
-7.29
-.70
-.71
3
2.000
1.183
.278
.350
-1.30
-1.29
5.30
5.29
5
-2.000
5
Scheffe
Bonferroni
-5.16
1.183
3
5
Lower Bound
.249
-4.000*
5
4
Sig.
5
5
Tukey
ScheffeHSD
(I-J)
Std. Error
Multiple
-2.000 Comparisons
1.183
3
1.183
.278
.350
-5.30
-5.29
1.30
1.29
3
4.000*
1.183
.018
.016
.70
.71
7.30
7.29
4
2.000
1.183
.278
.350
-1.30
-1.29
5.30
5.29