Question

Consider this example that can apply to an ANOVA:

A clinical trial is run to compare asthma education programs. Participants are randomly assigned to one of the asthma education programs and are counseled on the details of the assigned program. Participants follow the assigned education program for 8 weeks. The outcome of interest is days of absence.

Three asthma education programs are
included. 

Discuss why ANOVA could be used in analysis for this example, What would it tell you?

Can you think of an example for using ANOVA?

Answer 1

Assuming all assumptions of ANOVA are satisfied, we can apply ANOVA for the given example. Though ANOVA stands for analysis of variance it must be noted that it is used to compare several population means simultaneously. The test of significance based of t distribution is an adequate process only for testing the significance between two sample means. In situations when we have three or more population under consideration at a time then we use ANOVA for testing the significant difference between means of the population i.e., to check homogeneity of several means.

Here in this example participants will be experimental unit which will be divided in three groups(since three Asthama programs are available) each group will have ni participants such that sum(ni)=N and Asthma education program assigned are three treatments applied to each group.

Our null hypothesis will be all three Asthama program produces same number of days of absence. Alternative hypothesis will be all Asthama programs do no produce same number of days of absence.

Here, ANOVA examines whether all Asthama education program are homogeneous i.e. all program will have homogeneous effect on days of absence. Decision can be made from the value of F statistic in ANOVA table.

F= MST/MSE ~ F​​​​​​ 3,N-1 ......(since 3 treatments)

If F> F​​​​​​F3,N-1, then we may reject null hypothesis otherwise accept it. Thus in this way ANOVA helps.

Another example can be, Suppose a company has purchased 5 different machines and wishes to check whether one of them is faster than others in producing certain output then ANOVA can be used.