Demonstration of
OneWay ANOVA
(IndependentMeasures)


Example:
 This is hypothetical data from an experiment examining
learning performance under three temperature conditions.
There are three separate samples, with n=5 in each sample.
These samples are from three different populations of
learning under the three different temperatures. The dependent
variable is the number of problems solved correctly.
Independent Variable:
Temperature (Farenheit) 
Treatment 1
50F 
Treatment 2
70F 
Treatment 3
90F 
0
1
3
1
0 
4
3
6
3
4 
1
2
2
0
0 
Mean=1 
Mean=4 
Mean=1 

This is a oneway, independentmeasures design. It
is called "oneway" ("singlefactor") because "Temperature"
is the only one independent (classification) variable.
It is called "independentmeasures" because the measures
that form the data (the observed values on the number
of problems solved correctly) are all independent of
each other  they are obtained from seperate subjects.

Hypotheses:
 In ANOVA we wish to determine whether the classification
(independent) variable affects what we observe on the
response (dependent) variable. In the example, we wish
to determine whether Temperature affects Learning.

Demonstration:
 We demonstrate the logic of ANOVA by using this set
of data. Here they are again, this time shown as a ViSta
datasheet:
The most obvious thing about the data is that they
are not all the same: The scores are different; they
are variable.
Here are ViSta's summary statistics. Note, in particular,
the means and standard deviations.
Here are two plots of the data.
 The first is a histogram of the data. The three
groups are colored Red for T1, Green for T2 and Blue
for T3. (See the WorkMap
for rearanging the data to produce the histogram and
do the ANOVA.)
 The second is the diamond plot produced by the ANOVA
that we do later on.
Histogram

Diamonds

Are the groups different? This is what ANOVA trys
to answer. What do you think?
