Take a look at this box. You can see
each condition name in left most column. If you have given your conditions
meaningful names, you should know exactly which conditions these names
represent. You can find out the number of participants, the mean and
standard deviation for each condition by reading across each of the three
condition rows. You can also see things like the minimum and maximum value
in each condition, as well as confidence intervals and standard error.
In this Descriptive Statistics box,
the mean for the sugar condition is 4.20. The mean the mean for the a little
sugar condition is 3.60 and the mean for the no sugar condition is 2.20. The
standard deviation for the sugar condition is 1.30, the standard deviation
for the a little sugar condition is 0.89 and the standard deviation for the
no sugar condition is 0.84 (when rounded). The number of participants in
each condition (N) is 5.
We use ANOVA to determine if the
means are statistically different. But you don’t have to use ANOVA to find
out some basic information about mean differences. Compare your means. Which
one is the highest? Which is the lowest? If you were to find significant
differences with your ANOVA, what do these directional differences in the
means say about your results? In this example, the mean for the sugar
condition is 4.2 words whereas the mean for the no sugar condition is 2.2
words remembered. The mean for the A little Sugar Condition, 3.6, falls in
between these two. So just eyeballing it, we can see that there are more
words remembered in the Sugar condition. We need our ANOVA to determine if
the differences between condition means are significant. We need ANOVA to
make a conclusion about whether the IV (sugar amount) had an effect on the
DV (number of words remembered). But looking at the means can give us a head
start in interpretation.
This is the next box you will look
at. It shows the results of the 1 Way Between Subjects ANOVA that you
conducted. Take a loot at the Sig. value in the last column.
This value will help you determine
if your condition means were relatively the same or if they were
significantly different from one another. Put differently, this value will
help you determine if your IV had an effect. In this example, the Sig. value
is 0.027.
You can conclude that there is no
statistically significant difference between your three conditions. You can
conclude that the differences between condition Means are likely due to
chance and not likely due to the IV manipulation.
If the Sig value is less
than or equal to .05…
You can conclude that there is a
statistically significant difference between your three conditions. You can
conclude that the differences between condition Means are not likely due to
change and are probably due to the IV manipulation.
The Sig. value in our example is
0.027. This value is less than .05. Because of this, we can conclude that
there is a statistically significant difference between the mean number o
words remembered for all of our conditions (sugar, a little sugar, no
sugar).
The Sig value does not tell you
which condition means are different. It could be that only the sugar
condition is significantly different than the no sugar condition in terms of
number of words remembered. It could be that only the a little sugar
condition is significantly different than the no sugar condition. It could
be that all conditions are significantly different from each other. The Sig
value can tell us that there is a significant difference between some of the
conditions. It just cannot tell us which ones.
Researchers have solved this problem
by conducting post hoc tests. These tests are used when he have found
statistical significance between conditions but when we don’t know where the
significant differences are. These tests are not used when the results of a
1Way Between Subjects ANOVA are not significant because there is no need.
But when we do find a statistically significant result, when the Sig. value
is less than .05, we need to use these tests.
When you analyzed your data, you
might remember being asked to click on the Post Hoc button. This button
brought up a Post Hoc Multiple Comparisons box with many options to check.
These options represented various post hoc tests. Most of these tests have
strange names (like Bonferroni and Scheffe) but that’s just because they are
named after the people who invented them. You were asked to check two tests,
Tukey and Dunnett’s T3. You really could have checked as many as you liked.
The Tukey test is popular so we will focus on that one. If you find a
significant result with a 1Way Between Subjects ANOVA, and if your IV has 3
levels, you will need to use the results of a post hoc test like the Tukey
test to compare
ü
Condition 1 and Condition 2
ü
Condition 1 and Condition 3
ü
Condition 2 and Condition 3
Because of the fact that we found a
statistically significant result in our example, we would want to look at
the results of a post hoc test like Tukey. This will help us find out which
of our conditions were significantly different from each other. We conduct
post hoc tests like the Tukey to compare each of the following conditions.
ü
Sugar and No Sugar
ü
A little Sugar and No Sugar
ü
A little Sugar and Sugar
This is the place where you will
look to find the results of your post hoc tests. In the first column of this
box, you will see your condition names. The condition names appear in six
rows. These rows show the comparisons of various conditions. On the left
hand side of every other row, you will see a single condition name. On the
right hand side of each row, you will see a condition name. The statistics
that you see in the columns to the right of the first column show you the
comparison between the condition name on the left and each of the condition
names on the right.
In our example, the condition name
Sugar appears in the first column on the left hand side of the top row. The
condition name A little sugar appears to the right of it. If we read across
this particular row, we will see statistics that compare Sugar and A little
sugar conditions. We can also see the name No Sugar in the first column on
the right hand side of the second row. If we read across this particular
row, we see statistics that compare Sugar and No Sugar conditions.
Take a look at the Sig value when
reading across each row. The Sig. value will tell you whether the two
conditions that are being compared are significantly different. If the
conditions are significantly different, the Mean Difference value in the
corresponding row will also contain a star (*). There is more that one way
to determine significance when using this type of post hoc test.
You can conclude that there is no
statistically significant difference between the two conditions that are
being compared. You can conclude that the differences between condition
Means are likely due to chance and not likely due to the IV manipulation.
If the Sig value is less
than or equal to .05…
You can conclude that there is a
statistically significant difference between the two conditions being
compared. You can conclude that the differences between condition Means are
not likely due to chance and are probably due to the IV manipulation.
Looking at the Sig.
column in our example, we can see that most of the values are greater than
.05. However, there are two values that are 0.025. These values correspond
with the comparison between the Sugar and No Sugar conditions. For this
reason, we can conclude that the Sugar and No Sugar conditions are
significantly different in terms of words remembered. However, the other
condition comparisons are not significantly different from one another. This
means that the A little Sugar condition and No Sugar condition are not
significantly different. It also means that the A little Sugar condition and
Sugar condition are not significantly different.
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