I am a fan of explaining the heart of a statistical analysis conceptually with words and examples, not with math. Information Is Beautiful has a gorgeous new interactive, Diversity in Tech, that uses data visualization to present gender and ethnic representation among employees at various big-name internet firms.
I think this example explains why we might use Chi-Square Goodness of Fit. I think it could also be used in an I-O class.
So, what this interactive gives you is a list of the main, big online firms. And then the proportions of different sort of people who fall into each category. See below:
When I look at that US Population baseline information, I see a bunch of expected data. And then when I see the data for different firms, I see Observed data. So, I see a bunch of conceptual examples for chi-square Goodness of Fit.
For example, look at gender. 51% of the population is female. That is you Expected data. Compare that to data for Indiegogo. They have 50% female employees. That is your Observed data. Eyeballing it, you can guess that wouldn't be a significant chi-square. The two distributions are very similar. Again, this is a CONCEPTUAL introduction to what chi-square looks at, not a computation one.
Another important conceptual piece to chi-square is the fact that you need your O and E values to be pretty far apart in order to get a big test statistic. So, you also ask your students to compare: Which do you think would have a larger chi-square test statistic for Latino Employees: Amazon or Ebay? The Expected value is 18%. Since Amazon's 13% is closer to the Expected value of 18% than Ebay's 4%, we would expect Amazon to have a smaller X2 value than Ebay.
I bet you could also use this data while teaching I-O. One way to demonstrate fair hiring practices is to demonstrate that your workforce mimics the ethnic breakdown of America, or your state, or your region. As such, you could ask your students to pretend to be consultants and make recommendations for which firms have the biggest disparities, using this data as evidence.
I think this example explains why we might use Chi-Square Goodness of Fit. I think it could also be used in an I-O class.
So, what this interactive gives you is a list of the main, big online firms. And then the proportions of different sort of people who fall into each category. See below:
When I look at that US Population baseline information, I see a bunch of expected data. And then when I see the data for different firms, I see Observed data. So, I see a bunch of conceptual examples for chi-square Goodness of Fit.
For example, look at gender. 51% of the population is female. That is you Expected data. Compare that to data for Indiegogo. They have 50% female employees. That is your Observed data. Eyeballing it, you can guess that wouldn't be a significant chi-square. The two distributions are very similar. Again, this is a CONCEPTUAL introduction to what chi-square looks at, not a computation one.
Another important conceptual piece to chi-square is the fact that you need your O and E values to be pretty far apart in order to get a big test statistic. So, you also ask your students to compare: Which do you think would have a larger chi-square test statistic for Latino Employees: Amazon or Ebay? The Expected value is 18%. Since Amazon's 13% is closer to the Expected value of 18% than Ebay's 4%, we would expect Amazon to have a smaller X2 value than Ebay.
I bet you could also use this data while teaching I-O. One way to demonstrate fair hiring practices is to demonstrate that your workforce mimics the ethnic breakdown of America, or your state, or your region. As such, you could ask your students to pretend to be consultants and make recommendations for which firms have the biggest disparities, using this data as evidence.