Statistics with Sasa

Race has a long and complex history in the United States, perhaps first dating back to 1619 when some "20 and odd" Africans were first brought to the colony of Jamestown.  Since then our rich culture of immigration (some of it, unfortunately forced ) has resulted in a society where 40% of us can be considered "minorities." In fact, less than half of children under 15 are white , indicating a potential shift to a majority-minority society in the future. It goes without saying that minorities have made and continue to make enormous contributions to American society. Despite this, we as a country have a checkered past of treating them. From slavery to internment camps, from the transcontinental railroad to Jim Crow laws, the list really goes on. Given that some of these transgressions, like the Jim Crow laws, occurred just a generation ago, it is not hard to imagine a world where residual sentiments behind them still linger. This brings me to current events. Fro...

Climate change has far reaching impacts beyond the gradual warming of the earth. The ocean is becoming more acidic , coral reefs are dying , and species are going extinct at alarming rates. In particular, extreme weather events appear to be becoming more common in recent years. Evidence suggests that severe floods and droughts have increased  in certain regions of the United States. Anecdotally, just in the past few years, we've seen historic floods in Houston, the worst natural disaster in recorded history to hit Puerto Rico (Hurricane Maria), and devastating wildfires in Australia, just to name a few. I'm going to take a closer look and see if we can empirically show that flooding has gotten worse in frequency and magnitude in the Southern U.S. Interestingly, I found little scientific research on the subject. So basically. You heard it here first. Flooding Down South The Model I obtained data from the United States Geological Survey (USGS) for the stream/river networ...

It's been some 45 days since the White House declared COVID-19 a National Emergency and the bulk of us became largely confined to our homes. As people begin to agitate for the end of the quarantine and a number of states begin to open up, I thought I'd offer up a loose collection of data-driven thoughts on the quarantine we've all been experiencing. These insights are based on mobility data measured as Vehicle Miles Traveled (VMT). While this is an imperfect metric, we can use the reduction in VMT since before the pandemic as a rough proxy of how effectively we have been adhering to the quarantine. The Quarantine Was Effective, but Effectiveness Varied by State The first observation is that the quarantine was effective, which is probably obvious from a quick glance outside. Average mobility by county fell by approximately 65% when compared to January (the troughs you see are weekends). Some states adhered to the quarantine more seriously than others ...

Unless you live under a rock, you've heard of COVID-19, colloquially known as Coronavirus (or, if you prefer,  Caronavirus ). Your state may have multiple confirmed cases, and you may be under quarantine and working from home. You might even have it and passed it to others in your life . In any way, it has undoubtedly affected your life at this point as it has taken the world by storm: Perhaps the headline of Coronavirus in the United States has been the Federal Government's alleged mishandling of the virus as it reached our shores. From faulty test kits to contradicting statements from our Commander-in-Chief, it's hard to say that the response has been stellar. I wanted to see if we can statistically show that the government's conduct in these trying times has had a measurable impact on outcomes for U.S. residents. First, I'll start off by listing reasons why this exercise is a fair one and not some political witch-hunt. In the lead-up to the pandemic, the ...

To create my metric, I make use of a 2-parameter model pioneered by Viboud et. al . Specifically, it measures number of cases on day  t, C(t),  using the following parameters:  r  is a measure of growth rate,  A  is a constant, and the "deceleration of growth parameter" is given by $p = 1-\frac{1}{m}$, where  p  is between 0 and 1. Specifically,  p  has unique properties. If  p  is equal to 0, then the cumulative number of cases grows  linearly.  If  p  is equal to 1, then the cumulative number of cases grows  exponentially.  Everything in-between displays  sub-exponential  growth. Cases with sub-exponential growth can be modeled using the following formula: $C(t)=(\frac{r}{m}t+A)^{m}$ r  and  p  can be estimated by applying current data and nonlinear least squares (NLS) to the above formula. In practice, as  p  approaches 0, a plot of cumulative cases is...

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...