ABSTRACT
Aim: Upon completing the chapter, the learner should be able to perform an analysis of variance to compare the expected values of a continuous random variable between different groups.
6.1 Introduction An analysis of variance (ANOVA) can be performed to compare two or more parameters (expected values and variances). The possible objectives of this analysis might be to:
1. Compare the expected value of a continuous random variable in “m” different groups to assess the following hypothesis:
H m0 1 2:µ µ µ= = =
2. Determine which expected values are different among comparison groups to evaluate any of the following potential null hypotheses:
: ; : ; :µ µ µ µ µ µ µ µ µ µ= = + + + = +
3. Determine if the variability of a random continuous variable is the same between different groups to evaluate the following hypothesis:
H0 2 0:σα =
6.2 Data Structure Assuming that we have three groups or three selected groups, the database to compare the expected value of random variable Y would have the following structure:
The possible research questions for this study are:
1. Assuming that the information available is from all possible groups, the research question can be stated as follows: Does the expected value vary by group (μ1= μ2= μ3)? (Fixed effects model)
2. Assuming that the information available is from a random sample of all possible groups, the research question can be stated as follows: Is there any variation among all the groups (σα2
≠ 0)? (Random effects model)
6.3 Example for Fixed Effects To exemplify the research question for fixed effects (above), we are going to use the information from the previous database. As the bmig consists of three groups (normal, overweight, and obese), the research question would be the following: Are there differences in the expected age, according to the bmig categories?
