Chi-square Test: Insight from Using Microsoft Excel

The chi-square test is a non-parametric analysis involving two categorical variables. The null hypothesis for the chi-square test is best understood by looking at a real contingency table. I assembled one of these in Microsoft Excel as a demonstration. The experimental unit being counted in the contingency table is casinos. The first categorical variable was state where the casino was located – either Florida or New York. The second categorical variable was casino ownership – Native American or Other.

The null hypothesis for a chi-square test is always that column membership does not depend on row membership (and vice versa). What that means is our null hypothesis for this contingency table is that whether a casino is located in Florida or New York does not relate to whether or not it is owned by Native Americans.

In a chi-square test, the first thing you do is assemble an “observed” contingency table, which shows the actual values you found in your data. The next thing you do is assemble and “expected” contingency table. I did this in Excel and you can see them in the graphic below.

The chi-square is a non-parametric bivariate test between two categorical variables.

As mentioned in the graphic, you will notice that the marginals (meaning the column totals and row totals) are the same in the “observed” and “expected” tables. What is different is the values in the cells in the middle of the table. In the observed table, they are just the real actual data you observed. But in the expected table, they are calculated. For each cell, you take the product of the row total and the column total for that cell, and divide it by the grand total.

Once you assemble both these tables in Excel, you can use them to calculate a p-value and see if you will reject the null hypothesis or not. Let’s assume we set α at 0.05. In Excel, to calculate the p-value, you use the CHISQ.TEST function, which takes two arguments: the observed cells, and the expected cells. The graphic below gives more of an explanation.

You can calculate the p-value for a chi-square test in Microsoft Excel.

As you can see by the graphic, the result of our chi-square test is p=0.0417, which means at α=0.05, you would reject the null. This means that column membership (which state the casino is in) is indeed statistically significantly associated with row membership (Native American ownership or not).

Insight from Microsoft Excel

In statistical packages like SAS and R, you do not have to assemble the observed and expected contingency tables. You just refer to the variables in your dataset in your code, and the statistical software assembles these tables in its brain, and outputs the resulting p-value.

That’s why calculating a chi-square test in Excel can be particularly insightful. If you look at the values in the observed table, and then compare them to the expected table, would you have predicted that the result would be statistically significant? Do those values really look that different? Sometimes it’s obvious, but in this case, I really couldn’t predict what the result of the test would be.

If you want a detailed explanation of exactly how to do a chi-square test in Excel with an example, check out my LinkedIn Learning course, “The Data Science of Experimental Design”.

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Chi-square test is hard to grasp – but doing it in Microsoft Excel can give you special insight. Read about it on my blog!

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