The chi-square test of association

Week 8 wrap up and summary

The Chi-square test of association.

The chi-square test of association – testing for independence of samples.

Chi-Square tells us whether two groups have significantly different opinions, which becomes a very useful piece of data for survey research. It’s applied to cross-tabulations, which can look like this:


Fortunately, there is a variety of survey software or statistics programs, which will take the “observed” values and crunch everything for us. Here is an online example of just one of these programs …

Microsoft Excel has a CHITEST function, but it may require a bit of handwork. We would have to manually generate all the “expected” values, and all it does is give you the Total Chi-Square. To get the probability, we would have to pair it with the CHIDIST function, manually giving it the degrees of freedom.

So, to apply a Chi-Square to a survey, we must look at our question types. Chi-square can be used with any pair of single-answer discrete questions.

This would include demographics, Likert scales, cities, product names, dates once they’ve been grouped into periods, or numbers once they’ve been grouped into ranges. The answers would not need to be ordered, equal, or symmetrical — just discrete. This is why the Chi-Square is a convenient statistic for surveys.

A very useful tool!

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