All the tests we’ve done so far have involved sets of data for which we could find the mean and standard deviation. However, sometimes we only have frequencies or proportions. For example, let’s say that marketing researchers post an article about a new product on Facebook, Twitter, LinkedIn, and Instagram. They want to determine if followers are more likely to read the article from a particular social network.

The company has the following numbers of followers on Twitter, Facebook, and LinkedIn (in thousands):

Facebook: 1991 Twitter: 821 LinkedIn: 1733

After releasing the article, the marketing researchers found the following numbers of people clicked the link:

Number of people who click link (in thousands)

Facebook

19

Twitter

23

LinkedIn

15

z-tests and t-tests are parametric tests since they’re based on means and standard deviations. In this case, we need to do a non-parametric test to determine if the number of people who clicked the link to the article is what we would have expected based on the number of followers on each social network. This is the null hypothesis; the alternative hypothesis is that the number of people who clicked the link is different than what was expected.

In this case, we’ll do a chi-squared goodness-of-fit test (χ^{2}) to test the “fit” between observed and expected values.

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