ANOVA in SAS
Mean Comparison With More
Than Two Groups
Introduction
ANOVA (analysis of variance) tests are used
to compare the means of multiple groups
(as opposed to the t-test, which can only
be used for up to two groups).
An ANOVA tests Ho: all group means are
equal vs. Ha: at least one group’s mean is
different.
The ANOVA results do not tell you which
group is different, only whether a
difference exists.
ANOVA in SAS
Open SAS and use the infile statement to
input the data set relief.txt (this is also the
first data set of the INFILE tutorial).
If you don’t remember how to do this, here is
some code that may help:
data relief;
infile 'C:\Documents and Settings\My Documents\relief.txt';
input group $ time;
proc print data = relief;
run;
Once you print your data, notice that there
are three groups: A, T, M. The data are
from an experiment in which subjects were
given Aspirin, Tylenol or Motrin for
headaches. The time until relief was
measured for each subject. The question
of interest is: Does time to relief differ for
any of the treatments, or are they all the
same?
In other words:
Ho: µA = µT = µM vs.
Ha: at least one group mean is different
SAS Code for ANOVA
PROC ANOVA DATA = relief;
class group;
model time = group;
RUN;
QUIT;
To test our hypothesis,
we use the following
code in SAS:
• “class” tells SAS the classification variable. In general,
this is going to be the effect that you are studying. In this
case, the effect is “group.”
• “model” tells SAS the dependent variable. The general
format is “model Y = X” where Y is the dependent
variable, and X is the independent variable. In this case,
time to relief is dependent on treatment group.
• Often a “quit” statement is necessary, because SAS may
continue to run a procedure until either another one has
been run, or SAS has been told to quit.
Run the Program—Check Your Log
If your Log is free of error
messages, look at your output.
The first page of your output says that there
were three categories under the variable
“Group”: A T M.
It also tells you that there are 18
observations (it’s a good idea to doublecheck these numbers, to make sure no
data are missing).
Scroll down to the second page.
ANOVA Table in SAS Output
Interpreting the SAS Output
• The “Between SS” is under “Model” and
has a value of 2483.44.
• The “Within SS” is under “Error” and has a
value of 799.50.
• The degrees of freedom are listed under
“DF.”
• The F*= MSB/MSW = 1241.72/53.30 =
23.30. The p-value of this F* is found
under “Pr>F” and p < 0.0001.
Conclusions from ANOVA
Because the p-value for the test statistic (F*) is
less than alpha (0.05), we reject the null
hypothesis and conclude that at least two of the
groups’ means differ on time to relief.
Now the question is: which groups are different?
Answering this question requires multiple
comparisons, which can affect the Type-I error.
To correct for this, we can use the Bonferroni
Method.
The following code is exactly the same as before,
except a line has been added, requesting the
Bonferroni correction.
ANOVA Code with Bonferroni Method
PROC ANOVA DATA = relief;
class group;
model time = group;
means group / bon;
RUN;
QUIT;
The fourth statement requests that SAS use the
Bonferroni Method when comparing the means
of each category within the variable “group.”
Your SAS Output will be the same as previously,
but it will have an additional page.
Bonferroni Method Output
Interpreting Output
As stated in the SAS Output under the Bonferroni
tests, “Means with the same letter are not
significantly different.”
Because the Aspirin and Tylenol groups have the
same letter (A) under the heading “Bon
Grouping,” this indicates they are not
significantly different in mean time to relief from
headache.
The Motrin group, however, has a different letter
(B) under the “Bon Grouping,” which indicates
that the Motrin group differs significantly from
both the Aspirin and Tylenol groups. A brief
comparison of their means shows that those
who took Motrin had significantly quicker time to
relief (15 min) than the Aspirin (44 min) or
Tylenol (34 min) groups.
Conclusion
The code given in this section can be used
for all one-way ANOVAs, with slight
modification of variable names, etc., to
determine whether at least one group
differs significantly from the others.
The p-value from this test will tell you if at
least one group is different.