In which we demonstrate that you don't necessarily need a lot of math to do statistics

Statistical analyses can reveal a lot about the world in fields ranging from physics to health care to media. Which means a lot of people who never expected it now find themselves doing statistics. Good then that all statistical analysis boils down to just three questions. And none of them necessarily require a lot of math.

Really.

To prove it, let’s apply those three questions to this U.S. Census Bureau graphic, which shows the recent history of health insurance in the U.S.

[Source: U.S. Census Bureau]

Question 1: How big is it?

Start with measurement, for statistical analysis can only begin when we look at the world closely enough to quantify it. The graphic provides three kinds of measures. First, we have the percentage of people who are uninsured (the dots). This is broken out by time (year) and geography (states, DC and the total for the nation). It adds up to 416 data points.

Second, we have a derived measure – the differences between the years (the lines, 364 of them).

Finally, this graphic has categorical data points – the footnotes showing how many and which states adopted the Medicaid expansion (an optional provision of the Affordable Care Act, or ACA).

Altogether, this graphic answers, “How big is it?” 831 times.

Now, few people get excited about the measurements themselves. Most people reserve their excitement for the second question.

**Question 2: What difference does it make?**

People want to know what the numbers mean.

In this case, we want to know whether the ACA (aka Obamacare) succeeded in its goal of reducing the number of people without health insurance. Major provisions of the law took effect in 2014. Thus, we would expect to see its effects from 2013 to 2014, and then potentially again from 2014 to 2015. These post-law measures appear in blue, with measures for prior years appearing in gray.

The gray dots clump together, showing only relatively small changes in uninsured rates from one year to the next before the ACA went into effect. But, take a look at the blue dots. The wide separation shows the proportion of uninsured plummeted after the ACA became law.

Obamacare appears to have made a considerable difference, with huge improvements in the uninsured rate in state after state. But before we let ourselves get too enthusiastic, we must always attend to that third question.

**Question 3: Are you sure that’s not just dumb luck?**

There are many versions of this last question because statistical thinking can be tricky. This is often where the math comes in. But this case doesn’t call for any.

First, the pattern is the same in every state, except Massachusetts (I’ll explain below). Prior to the ACA, we see little to no movement in the uninsured rate. Then after, we see a huge change all in the direction of improvement. When a phenomenon shows up over and over again, you start to suspect it might be real.

Yet, could it be a coincidence that some sudden demographic shift or similar change in the nation accounted for the improvement? No. Because, if the improvement was due to something other than the law, you would expect to find that change in Massachusetts, too. But Massachusetts – which already had its own health insurance law (in fact, the model for Obamacare) – experienced only slight movement in the uninsured rate.

We can’t look to the economy to explain this change, either. The 2008-2015 time frame includes considerable economic swings. We don’t see big swings in the uninsured rate until after Obamacare.

Now examine the Medicaid expansion data. States with it did better (appear higher in the graph) than states without. And among those states in the lower half of the graph, those few that included the Medicaid expansion (like Arizona, New Mexico and Nevada) did far better than their peers.

To sum it up: After Obamacare took effect we saw unprecedented improvements in the uninsured rate in every state, except where a version of the law had been in effect already. States that enacted the full law did better than those that rejected the Medicaid expansion.

To sum it up even further: If the goal was to reduce the population of uninsured in the nation, Obamacare delivered.

Statistical analysis says so.

Statistical analysis is really just a disciplined way of looking at the world. It begins with careful measurement and then looks for patterns and then moves through steps to make sure the patterns we find really mean what we think they mean. It is often a complex, mathematical process, but it can be as simple as drawing the right picture.