Explaining Statistical Tests – Chi Square

This is a bit more exotic than some of the previous tests.  A test that uses Greek letters, crazy!   In all seriousness though, this is a test that a lot of non-statistics folks have maybe heard of once or twice.

Chi Square Test is used to test the independence of categorical variables.  That is, this test will tell whether there is a difference between groups for a particular outcome category.  If you have two categories that you’re trying to determine difference with two options, this might be the test for you.

I’ve been using retail examples, so let’s continue with that.  Let’s say we want to test two different sales displays, so we set up a sales display in 2 different stores with reasonably similar profiles.  We then track how many customers purchase the item that’s on sale and compare the 2 stores.  So you may end up with something like of 57 people at store 1, 20 purchased the item, and out of 73 people at store 2, 28 purchased the item. Thus, respectively, 37 and 45 did not purchase the item.  Chi Square test can tell you whether these are significantly different from each other (and thus whether one sale is better).

So far, we’ve looked at what are called “parametric” tests or tests based on the normal distribution.

  1. T test – category vs continuous
  2. F Test (ANOVA) – categories vs continuous
  3. Regression – continuous vs continuous
  4. Chi Square – category vs category


  1. Independent samples
  2. Adequate sample size

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