A one-way ANOVA is used to determine whether or not there is a statistically significant difference between the means of three or more independent groups.
This tutorial provides a step-by-step example of how to perform a one-way ANOVA in SAS.
Step 1: Create the Data
Suppose a researcher recruits 30 students to participate in a study. The students are randomly assigned to use one of three studying methods to prepare for an exam.
The exam results for each student are shown below:
We can use the following code to create this dataset in SAS:
/*create dataset*/ data my_data; input Method $ Score; datalines; A 78 A 81 A 82 A 82 A 85 A 88 A 88 A 90 B 81 B 83 B 83 B 85 B 86 B 88 B 90 B 91 C 84 C 88 C 88 C 89 C 90 C 93 C 95 C 98 ; run;
Step 2: Perform the One-Way ANOVA
Next, we’ll use proc ANOVA to perform the one-way ANOVA:
/*perform one-way ANOVA*/ proc ANOVA data=my_data; class Method; model Score = Method; means Method / tukey cldiff; run;
Note: We used the means function to specify that a Tukey post-hoc test should be performed if the overall p-value of the one-way ANOVA is statistically significant.
Step 3: Interpret the Results
The first table we want to analyze in the results is the ANOVA table:
From this table we can see:
- The overall F Value: 5.26
- The corresponding p-value: 0.0140
Recall that a one-way ANOVA uses the following null and alternative hypotheses:
- H0: All group means are equal.
- HA: At least one group mean is different from the rest.
Since the p-value from the ANOVA table (0.0140) is less than α = .05, we reject the null hypothesis.
This tells us that the mean exam score is not equal between the three studying methods.
SAS also provides boxplots to visualize the distribution of exam scores for each of the three studying methods:
From the boxplots we can see that the exam scores tend to be higher among students who used studying method C compared to methods B and C.
To determine exactly which group means are different, we must refer to the final table in the output that shows the results of the Tukey post-hoc tests:
To tell which group means are different, we must look at which pairwise comparisons have stars (***) next to them.
From the table we can see that the mean values for groups A and C are statistically significantly different.
We can also see the 95% confidence interval for the difference in mean exam scores between group A and C:
95% Confidence Interval for Difference in Means: [1.228, 11.522]
Step 4: Report the Results
Lastly, we can report the results of the one-way ANOVA:
A one-way ANOVA was performed to compare the effect of three different studying methods on exam scores.
A one-way ANOVA revealed that there was a statistically significant difference in mean exam score between at least two groups (F(2, 21) = [5.26], p = 0.014).
Tukey’s HSD Test for multiple comparisons found that the mean value of exam score was significantly different between method C and method A (95% C.I. = [1.228,11.522]).
There was no statistically significant difference in mean exam scores between method A and method B or between method B and method C.
The following tutorials provide additional information about one-way ANOVAs: