Explaining Statistical Tests – ANOVA

My last post was explaining T tests.  In short, T test is a test of difference.  ANOVA is the T test’s bigger and more complicated cousin that still tests difference.  T test should only be used with one or two groups, but what if you have 3 or more?  Enter ANOVA!

The challenge with ANOVA is that you can only conclude whether there are differences between at least one of the groups.  For example, if you have 5 groups and there’s only a difference in one of them and the rest are the same, you’ll get the same result in ANOVA as if there are 3 different groups.

One might ask, so why not just do t tests for all the groups?  Well, because it’s wrong.  The easiest way to explain this is that each t test has the possibility of error in it, and for each additional test, the error increases, so your chances of drawing wrong conclusions increase with more tests.

But fear not, we can do what’s called a “multiple comparisons” test with an ANOVA test, so we can determine whether there’s difference and protect ourselves against wrong conclusions!

Example

In the T test writeup, I used the example of testing out a particular product my doing a test sale in 50 stores.  Imagine if you now wanted to test your design of the store product placement.  In one store, you wanted to set up your display by the jewelry, in another store by the men’s shoes, another store by the escalator, another store by the suits and another store by the t shirts.  You could use an ANOVA test to see if there’s any significant difference between these approaches and then a multiple comparisons (like Tukey’s HSD) to identify which one(s) are different.

Assumptions

  1. Normal distribution of variance
  2. Homoscedacity – equality of variances
  3. Independent random samples
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