Illuminating Statistical Analysis Using Scenarios and Simulations

13Rescaling to Standard Errors

You can see from the previous histogram that the distribution of sample proportion differences approximates a normal distribution, and indeed they do in general. So, there is a corresponding “trick” formula that can be used, which we'll look at next, followed by determining -values using standard errors and the standard normal distribution.

The formulaic method we'll explore in the next few chapters serves the same purpose as the “simulation results histogram eyeballing” method we just used. The formulaic method calculates the number of standard errors for the difference between two sample proportions, and then determines the -value for that number of standard errors of the standard normal distribution. The below formula does the first step by rescaling a proportion difference into the unit of standard errors. It is simply the proportion difference divided by the appropriate standard error, yielding the number of standard errors, #SEs, for the sample proportion difference. This is called standardizing.

is the first sample proportion, is the second ...