# Is Chi-Square Correct

I took bacteria samples at 30 grocery stores. Each grocery store was tested for 3 different bacteria types. I then taught a foodborne illness class to the managers of the grocery stores. After teaching this class I re-sampled the areas at each grocery store for the 3 types of bacteria. I want to test if the foodborne illness class reduced the presence of the bacteria (which is measured as positive or negative).

Below is an example of my data set. I read the Chi-Square can be good for answering a question similar to this. But I'm a little confused because each participant (i.e., grocery store) has 3 bacteria tests. So I don't know how to run a test on this. Any help would be greatly appreciated.

I just made up the data on the following table. But the real data set looks the same with 30 groceries instead of 3.

• Even without formal statistics, you can see you do not have evidence from those 9 tests that the foodborne illness class reduced the presence of the bacteria. None of the Restaurants/Grocery stores saw an improvement across the three bacteria, and none of the bacteria saw an improvement across the three Restaurants/Grocery stores Commented Jun 6, 2019 at 20:22
• sorry I should have clarified that I just made that table up to demonstrate what my actual table looks like Commented Jun 6, 2019 at 20:49

In a sense, the data you have here is three-dimensional. The dimensions are the grocery stores, the bacteria type, and pre- and post-sampling. For a complete analysis of your data, I would suggest a Log-Linear Analysis. A good online tool for this (which also explains the motivation behind it) can be found here: http://vassarstats.net/abc.html

For your purposes, though, it seems like you will not need this level of detail. Depending on how much data you have, it might not be statistically significant and the numbers could be misleading. I would suggest doing a Chi-Square analysis for each bacteria instead.