Video Tutorial – Calculating Expected Counts in a Contingency Table Using Joint Probabilities

In an earlier video, I showed how to calculate expected counts in a contingency table using marginal proportions and totals.  (Recall that expected counts are needed to conduct hypothesis tests of independence between categorical random variables.)  Today, I want to share a second video of calculating expected counts – this time, using joint probabilities.  This method uses the definition of independence between 2 random variables to form estimators of the joint probabilities for each cell in the contingency table.  Once the joint probabilities are estimated, the expected counts are simply the joint probabilities multipled by the grand total of the entire sample.  This method gives a more direct and deeper connection between the null hypothesis of a test of independence and the calculation of expected counts.

I encourage you to watch both of my videos on expected counts in my YouTube channel to gain a deeper understanding of how and why they can be calculated.  Please note that the expected counts are slightly different in the 2 videos due to round-off error; if you want to be convinced about this, I encourage you to do the calculations in the 2 different orders as I presented in the 2 videos – you will eventually see where the differences arise.


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