Now go back and
try Analyze > Compare Means > OneWay ANOVA. A potential factor
variable should now be available for you. Put that into the Factor window
and select your DV. Then press OK to run a Oneway ANOVA.
You should get
results that look like this:
These results
show you the variance (Mean Square = "mean squared deviations from
the mean" = variance) between groups and the variance within groups.
Use a calculator and divide the MS(Between) by the MS(Within). Compare
that value to the F statistic. Should be very close, because that's
what the F is  a ratio of the variance between groups to the variance
within groups.
APA
Style for OneWay ANOVA Results
To report the
results of a oneway ANOVA in APA style, you need to report the F, two
degrees of freedom, and the pvalue. The two degrees of freedom you need
to report are the betweengroups df and the withingroups df.
You could write:
A oneway
ANOVA was used to test for preference differences among three sizes
of a candy bar. Preferences for candy bar differed significantly
across the three sizes, F (2, 27) = 5.77, p = .008.

Note the betweengroups
df comes first, and the withingroups df comes second.
Post Hoc Tests
A major limitation of the results
from a oneway ANOVA is that you don't know how the means differ,
you just know that the means are not equal to each other. To solve this
little mystery, you can use posthoc tests. Posthoc means "after
this" because this is a test you conduct after you already know that
there is a difference among the means you are comparing.
Select Analyze > Compare
Means > Oneway ANOVA again, but this time press the "Post Hoc"
button. The following screen appears:
As you can see
from this screen, there are several posthoc tests available. The one
most appropriate to most of the questions you'll be asking is the "Tukey"
test, also known as the Tukey "honestly significant difference (HSD)"
comparison. Note: this is "Tukey," named after John Tukey,
not "Turkey" as in Thanksgiving.
Given a set of
3 means, the Tukey procedure will test all possible 2way comparisons:
1&2, 1&3, and 2&3.
The
multiple comparison (fishing expedition) problem
Ordinarily, there
is a problem with conducting three comparisons in a row. The problem is
that with each additional test, it becomes more likely that you will obtain
one statistically significant result just by chance. Think of it
as a slot machine. If you pull the slot machine arm 4 times, you are 4
times as likely to hit the jackpot given a completely random process.
If you do 4 tests of statistical significance, you are 4 times as likely
to obtain one p<.05 result when there is no real difference
between your means. This is called the "fishing expedition problem"
because it's like you're casting your line out again and again, just hoping
to snag something that's significant. There are a number of methods to
deal with this problem, and each one is a kind of post hoc test. Each
method is optimized for a particular set of circumstances. What every
method does is to make an adjustment to the obtained significance
level (pvalue) to make it harder for you to obtain a p<.05.
This is like pulling the slot machine handle 4 times and having the slot
machine say "I know you just tried 4 times, so I'm making the odds
of winning harder." The Tukey method is optimized for the situation
in which you would like to test all possible pairwise comparisons
(comparing sets of two) among your means. Select the Tukey option and
press Continue.
Now click on Options
and check the box under Statistics marked "Descriptive". You
will need it to report confidence intervals. Click Continue and then OK.
You should obtain the following new table:
Descriptives 
pref 

N 
Mean 
Std.
Deviation 
Std.
Error 
95%
Confidence Interval for Mean 
Minimum 
Maximum 
Lower
Bound 
Upper
Bound 
fun 
10 
5.4100 
.58775 
.18586 
4.9896 
5.8304 
4.20 
6.20 
regular 
10 
4.4300 
.87693 
.27731 
3.8027 
5.0573 
3.40 
6.50 
king 
10 
5.1100 
.44335 
.14020 
4.7928 
5.4272 
4.50 
5.70 
Total 
30 
4.9833 
.76207 
.13913 
4.6988 
5.2679 
3.40 
6.50 
This table provides
you with the mean values of your three groups (5.41, 4.43, and 5.11) and
also the confidence intervals for each mean. Below that table is the ANOVA
table from before, which has not changed, and next is another new table:
Multiple
Comparisons 
pref
Tukey HSD 
(I)
size3 
(J)
size3 
Mean
Difference (IJ) 
Std.
Error 
Sig. 
95%
Confidence Interval 
Lower
Bound 
Upper
Bound 
fun 
regular 
.98000^{*} 
.29563 
.007 
.2470 
1.7130 
king 
.30000 
.29563 
.574 
.4330 
1.0330 
regular 
fun 
.98000^{*} 
.29563 
.007 
1.7130 
.2470 
king 
.68000 
.29563 
.073 
1.4130 
.0530 
king 
fun 
.30000 
.29563 
.574 
1.0330 
.4330 
regular 
.68000 
.29563 
.073 
.0530 
1.4130 
*.
The mean difference is significant at the 0.05 level. 
This output identifies
your DV ("pref" for preference rating of candy bar) and tells
you the type of multiple comparison adjustment it is using ("Tukey
HSD"). If you attached text labels to the values of your new IV,
you'll get them like I did above.
There are several
comparisons listed in the table above. In the first row, you can see the
comparison between funsized bars and regular bars. The difference
between the means of these two groups is .9800. Following this row across,
we see that this difference was statistically significant (p =
.007). In the table above, we see that the significant overall ANOVA we
found earlier was due to a difference between just two groups: fun vs.
regular. None of the other comparisons are significant.
This is somewhat
consistent with our conclusions from the plot: the regularsized bar was
liked less than either of the other two bars, which did not differ from
each other. What is slightly different is that we expected that the regular
bar would be liked significantly less than both the funsized and
the kingsized bar. In fact, the regularsized bar was liked significantly
less than the funsized bar (p = .007) but the difference was not
quite significant for the kingsized bar (p = .073).
There is another
table of output as well:
This table is
a handy summary of the major differences among the means. It organizes
the means of the three groups into "homogeneous subsets"  subsets
of means that do not differ from each other at p<.05 go together,
and subsets that do differ go into separate columns. Groups that don't
show up in the same column are significantly different from each other
at p < .05 according to the Tukey multiple comparison procedure.
Notice how the "regular" group and the "fun" group
show up in separate columns. This indicates that those groups are significantly
different. The kingsize group shows up in each column, indicating that
it is not significantly different from either of the other two groups.
To report these
results, you could write:
A oneway
ANOVA was used to test for preference differences among three sizes
of a candy bar. Preferences for candy bar differed significantly
across the three sizes, F (2, 27) = 5.77, p = .008.
Tukey posthoc comparisons of the three groups indicate that the
funsize group (M = 5.41, 95% CI [4.99, 5.83]) gave significantly
higher preference ratings than the regularsize group (M
= 4.43, 95% CI [3.80, 5.06]), p = .007. Comparisons between
the kingsize group (M = 5.11, 95% CI [4.79, 5.43]) and the
other two groups were not statistically significant at p
< .05.

Note how the confidence
intervals are presented: in brackets, after each mean, with the degree
of confidence stated explicitly ("95% CI").
