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.
In this Descriptive Statistics box,
the mean for the caffeine condition is 5.40. The mean the mean for the juice
condition is 7.20 and the mean for the beer condition is 9.40. The standard
deviation for the caffeine condition is 1.14, the standard deviation for the
juice condition is 1.10 (when rounded) and the standard deviation for the
beer condition is 1.14. 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 beer
condition is 9.4 hours of sleep whereas the mean for the caffeine condition
is 5.4 hours of sleep. The mean for the juice condition, 7.2, falls in
between these two. So just eyeballing it, we can see that there are more
hours slept in the beer condition when compare to the others. 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 (drink
type) had an effect on the DV (number of hours slept). But looking at the
means can give us a head start in interpretation.
This is the next box you will look
at. It contains info about the 1-Way Within Subjects ANOVA that you
conducted. There are many different variations of this test. Most
undergraduates use the “Wilks’ Lambda” variation. So, unless you are
instructed otherwise, it is likely that you will want to read from only the
Wilks’ Lambda row.
Take a look at the Sig value,
presented in the last column. Make sure you are reading from the Wilks’
Lamba row. This value will tell you if the three condition Means are
statistically different. Often times, this value will be referred to as the
p value. In this example, the Sig value in the Wilks’ Lamba row is 0.032.
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
0.032. This value is less than .05. Because of this, we can conclude that
there is a statistically significant difference between the mean hours of
sleep between some or all of our conditions (caffeine, juice and beer).
The Sig value does not tell you
which condition means are different. It could be that only the caffeine
condition is significantly different than the juice condition in terms of
hours of sleep. It could be that only the caffeine condition is
significantly different than the beer 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
1-Way Within Subjects ANOVA are not significant.
Undergraduates are often instructed
to conduct Paired Samples T-Tests to make post hock comparisons when they
find significant results in 1-Way Within Subjects ANOVAs Paired Samples
T-Tests have already been presented in this book. If you find a significant
result with a 1-Way Within Subjects ANOVA, and if your IV has 3 levels, you
will need to conduct three additional Paired Samples T-Tests. These test
will be used 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 conduct
three additional Paired Samples T-Tests. These tests would help us find out
which of our conditions were significantly different from each other. We
would conduct Paired Samples T-Tests to compare each of the following.
ü
Caffeine and Juice
ü
Caffeine and Beer
ü
Juice and Beer
You can follow the instructions in
the chapters on Paired Samples T-testing to conduct your three post hoc
tests. But there is one thing that you should be aware of. Instead of using
the value 0.05 to decide if we had reached statistical significant, we would
instead use the value 0.017 as the cut off. This means that we would compare
our Sig (2-Tailed) value with 0.017. If the Sig(2-Tailed) value generated in
a particular paired samples t-test was greater than 0.017, we can conclude
that there is no statistically significant difference between the particular
conditions for that test. If the Sig (2-Tailed) value generated in a
particular paired samples t-test was less than or equal to 0.017, then we
can conclude that there is a statistically significant difference between
those particular conditions.
The more significance tests that you
conduct, they higher probability you will find a significant result when one
does not exist in reality. When we do three Paired Samples T-Tests, we
increase our chances of finding a significant result when one doesn’t exist.
To account for that, we divide .05 by the number of tests that we are
conducting, 3 tests.
.05 divided by 3 = 0.017
That’s where we come up with that
number and that’s why we use it. If we were doing more than 3 tests, we
would divide .05 by that number.
**
Background |
Enter Data |
Analyze Data |
Interpret Data |
Report Data
** |