Database Reference
In-Depth Information
3.3.6 ANOVA
The
hypothesis tests
presented in the previous sections are good for analyzing
means between two populations. But what if there are more than two populations?
Consider an example of testing the impact of nutrition and exercise on 60
candidates between age 18 and 50. The candidates are randomly split into six
groups, each assigned with a different weight loss strategy, and the goal is to
determine which strategy is the most effective.
• Group 1 only eats junk food.
• Group 2 only eats healthy food.
• Group 3 eats junk food and does cardio exercise every other day.
• Group 4 eats healthy food and does cardio exercise every other day.
• Group 5 eats junk food and does both cardio and strength training every
other day.
• Group 6 eats healthy food and does both cardio and strength training
every other day.
Multiple
t
-tests could be applied to each pair of weight loss strategies. In this
example, the weight loss of Group 1 is compared with the weight loss of Group 2, 3,
4, 5, or 6. Similarly, the weight loss of Group 2 is compared with that of the next 4
groups. Therefore, a total of 15
t
-tests would be performed.
However, multiple
t
-tests may not perform well on several populations for two
reasons. First, because the number of
t
-tests increases as the number of groups
increases, analysis using the multiple
t
-tests becomes cognitively more difficult.
Second, by doing a greater number of analyses, the probability of committing at
least one type I error somewhere in the analysis greatly increases.
Analysis of Variance (
ANOVA
) is designed to address these issues. ANOVA is a
generalization of the hypothesis testing of the difference of two population means.
ANOVA tests if any of the population means differ from the other population
means. The null hypothesis of ANOVA is that all the population means are equal.
The alternative hypothesis is that at least one pair of the population means is not
equal. In other words,
•
:
•
:
for at least one pair of
i
,
j
