• ### Unit 10: Chi-Square

You open a bag of plain M&Ms and your friend opens his bag of peanut M&Ms, and you immediately notice that the two bags appear to have different proportions of the different colors. Each of you calculates the proportions of each color, and you are surprised to see that they are quite different for the two candy types. You wonder if these bags are just unusual - maybe the machine was out of whack at the factory when the bags were filled - or if the M&M people intentionally put different proportions of colors into the plain M&M bags compared to the peanut M&Ms.

While this example is not exactly akin to the quest for curing world hunger, it poses a question about categorical data that actually has many practical and important implications. Up to this point, we have only been able to do hypothesis tests for one proportion against a particular value, or for the equality of two proportions. But Unit 10 allows us to compare multiple proportions. In our example, we can compare the proportions of brown, blue, red, orange, green, and yellow candies all at the same time. We use the chi-square procedures for doing this.

The chi-square procedures have been used to test Mendelian genetics, beverage preference tests, and whether drivers of red cars really do get more tickets than other drivers.

Completing this unit should take you approximately 4 hours.