An analysis of variance is a statistical method for comparing the effect of the levels of a single factor or multiple factors on a response variable.
Use: Suppose you work in a hospital and you are interested in comparing four flavors that are added to a particular medicine. You do a blind study with a large number (>30) of children, and you will probably see variation in what flavors the kids like – or don’t like. The question that you are trying to get an answer to is: Is one (or more) of the flavors significantly favorable among children The operative word is ‘significantly.’ You might want to start with writing the alternative hypothesis statement:
Alternative Hypothesis Statement: There is a significant difference in one or more of the flavors.
Hypothesis Statement: There is not a flavor, or flavors that is significantly different than the others. You are really hoping to reject the null because you really are trying to find a flavor that kids like. If you fail to reject the null, doesn’t mean that your experiment failed. Instead, it means that you learned something – perhaps not what you had hoped to learn. You also learned that of those particular four flavors, none of them significantly stood out. If however, you find that you have rejected the null hypothesis, you have learned that one or more of the flavors did stand out as being significantly better than the others.
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