I am trying to model election data.
Say you have a state that is 50-50 Dem-Rep and the state has 100 districts.
Even though the state is 50-50, turnout will vary by district, and plotting the histogram of the vote-share of these districts, they should naturally form a Gaussian centered at 50%. Let’s assume a standard deviation of 20.
Now assume voter behavior changes and the state is 70% Democrat. With such a large standard deviation, the resultant histogram will be skewed.
How do I quantify or show the skewness? What function or process can I use to plot this?
Using excel, one can use the binom.inv function, but the standard deviation is 5 for the built-in 50-50 example, and shifting the state to 70% Democrat will not skew the distribution much because the standard deviation is so small. I also don’t want discrete values.
I’m thinking of a bag of marbles with 70% blue and 30% red, but this does not allow for changes in standard deviation. As you can see, I’m not sure how to set up this problem.