Statistics with Sasa

Recently, I had a discussion with a friend about income inequality and how it relates to the racial wage gap.  I found this conversation particularly relevant given the current Democratic primary race, where wealth inequality has been a hot-button issue  among the frontrunners .  The logic behind how one affects the other is simple. Certain minorities tend to be poorer on average than whites, so policies that improve income inequality will disproportionately affect minorities and work to close the racial wage gap.  The question at the forefront of our conversation was: exactly how much would policies that fix income inequality also close the racial wage gap? To get some clarity on the question, I set out to do a simple thought experiment. In it, I first created a hypothetical world with two races and 11,500 people: 10,000 white people and 1,500 black people. I then simulated a sample income distribution using  Census Bureau data  on income by race (h...

This article will teach you everything you need to know about drawing your very own realistic sample income distribution using two commonly available metrics: mean income and Gini index.  Let me preface my article by saying I rely on an assumption that incomes can be approximated using a lognormal distribution.  That's not an uncommon sentiment , and a visual inspection shows that it's not a crazy assumption: Example lognormal distribution Example income distribution Armed with this assumption, creating a sample income distribution is a simple exercise if you know the arithmetic mean and standard deviation of the distribution in question.  Given these two parameters, one can calculate lognormal mean and standard deviation with the following formulas:  $\mu = ln(\frac{E[X]^2}{\sqrt{Var[X] + E[X]^2}})$ $\sigma^2 = ln(1+\frac{Var[X]}{E[X]^2})$ Finding mean income for a society is pretty easy. Finding the standard deviation of income, howev...