The ANOVA (Analysis of Variance) technique is a statistical method that can be used to compare whether the means of three or more populations are equal. The ANOVA test can be carried out by calculating the value of the F-statistic. This requires calculating the sum of squares due to treatment and the sum of squares due to error. We now list out some of the merits and demerits of the ANOVA technique.
Advantages of ANOVA:
- Whereas the Z test can only be used to compare the means of two populations, the ANOVA test can be used to compare the means of three or more populations.
- If there are two different treatments/factors affecting the dependent variable, then we can use the two way ANOVA test to analyse the effect due to each treatment. The test will tell us whether the difference due to each of the treatments is significnt or not.
- We can check equality of three or more populations means by repeatedly applying Z test pairwise. But this increases the Type 1 error. On the other hand, the same comparison done by the ANOVA technique, has low Type 1 error. This means that ANOVA test is a statistically powerful test.
- The ANOVA method is used in clinical testing to check for the effectiveness of experimental medicines.
- The calculations involved in calculating the F statistics are easy and involve elementary operations such as squaring, summing up and dividing. The decision criteria for rejecting or accepting the null hypothesis are easy to understand.
Disadvantages of ANOVA:
- It often happens that the parent populations do not follow the normal distribution. For example, the lifetimes of products generally follow the Weibull distribution. In such cases the ANOVA method cannot be used. For instance, we may not be able to use the ANOVA technique to compare the mean life of bulbs produced by three companies.
- If there are two or more dependent variables then the ANOVA technique cannot be applied. The MANOVA test must be used in such cases.
- It rarely happens that all the population variances are equal. If the assumption of homoscedasticity is violated then the use of ANOVA cannot be justified.
- If the null hypothesis is rejected we can only conclude that some population means are unequal. The ANOVA test does not tell us anything about which of them are unequal. Some post hoc tests must be carried out in order to know about that.
- Checking all the background assumptions such as independence, normality, homoscedasticity, etc. is in and of itself a difficult task.
- Although the calculations involved are elementary they are still tedious to peform by hand. But ANOVA tests are usually carries out using statistical software so this is not a huge barrier.