May 20, 2016

Right to Work, more recent data

So, what's the argument over?

Do Right-to-Work laws fulfill their claimed benefits to workers? (Executive summary: They don't). Arguments in favor of right-to-work (RTW) boil down to claiming a better overall life for ordinary workers in a state. I'm going to explain my personal bias: No law should ever be made without compelling need. Thus, the entire burden of proof is not that a law will not make things any worse, it is that a law must make things better. This is why I'm not explicitly testing anti-right-to-work claims. Anti-any-law automatically is favored as the "null hypothesis". Of course, some laws are trivial to justify. The damage done to people and society by practices such as child prostitution are so enormous, and the moral issue so clear-cut, that it is trivial to show an overriding social need for a law against such practices. When it comes to labor law, things can start to become less immediately clear-cut.

Let's Talk Money

All State Differences
Median Income
Orange: Right-to-work state does better.
Blue: Non-RTW state does better.

One conventional measurement that dominates the argument about right-to-work is income. If you know me, though, you'll already know that I will not look at them in conventional ways. Attempts to attack or defend RTW based on "average" incomes are just plain silly. It's easy to see how. The "average" is only a good representation if income is evenly distributed, which it isn't. A very small portion of Americans in any state have much higher incomes than most of that state does. Instead of average, I will use median. The median is literally the number in the middle. Half of the households in a state makes no more than the median, half make no less than the median. Thus, it represents a truer estimate when the data is highly skewed.

Okay, so now that I've chosen median income (for 2014, since all data for 2015 isn't finalized, yet at the US Census) as the basis of comparison (conveniently available from the Burea of Labor Statistics, how to compare? One way is to aggregate the two groups of states (RTW vs. non-RTW), subtract one aggregation from the other, et voila! But "simple" isn't always so simple. If there is a difference between the two, is that difference meaningful? The data covers all the possible comparisons (all 50 states for that year). What aggregation should be used?

There are only 50 states. Of these 24 were RTW in 2014, 26 were not. That's not much. That's only 624 pairwise comparisons of states. We have spreadsheets in the modern day, so 624 subtractions are nothing. Okay, so I can do 624 subtractions of one state's median wage from another's, then what? Aggregate the subtractions and present column charts with error bars and all kinds of statistical gobbie-goo?

I could, but it would only hide more than reveal. After all, when I've got that few points of data, why not just present them all and let the reader see directly? That's what I did. The first figure displays every single comparison, grouped in "income difference" brackets. Orange columns are where an RTW state had a higher median income than a non-RTW state. Blue columns are the other way around. Orange = RTW better. Blue = RTW worse. If you mouse over, you'll see the limits of each bracket and the actual number of comparisons that fell into that bracket. Overall, an RTW state was better in 145 comparisons. A non-RTW state was better in 479 comparisons. So, that's a 73% disadvantage to RTW. Does that mean anything?

Let's look at it another way, what is the possibility that this difference could occur by random chance? If it is likely to have just been random chance, then we shouldn't let the difference lead us to any conclusions. I used a method called "bootstrapping" to estimate the probability that this outcome was by random chance. You can look up bootstrapping in any statistics textbook if you are really into the nuts and bolts. To make a long story shorter, it turns out that the probability of this outcome just being random chance is roughly 0.0004. Statistical "significance" begins when probability is equal to or less than 0.05. We can safely exclude random chance from explaining this outcome

All State Differences
Cost-of-Living Adjusted Median Income
Orange: Right-to-work state does better.
Blue: Non-RTW state does better.

But money goes out, too.

However, as Mark Twain long ago tried to point out in A Connecticut Yankee, income is only half the story of individual prosperity. If you make twice as much money as the cobbler in the next village but have to pay twice as much for everything, you're no better off than the cobbler in the next village, no matter how big your income might look before you pay your bills. A more accurate idea of the effect of RTW is to factor in cost of living as a relative state ratio. Thus, a more expensive state (New York) would have a 2014 cost of living at 1.316, while a cheaper state (Oklahoma) would have one of 0.921. What this means is that an income of $50,000 in New York would be roughly equivalent to an income of $35,000 in Oklahoma. The New Yorker might make more money on paper, but he'd be no better off than a Sooner making $15,000 less a year! That's a pretty important factor. I do have to caution that statewide costs of living are very approximate, and it is easy to find exceptions. Manhattan would be even worse, for example.

When we factor in cost of living to median income, the picture changes. RTW states now have a slight advantage. Cost-of-living adjusted median wages are better in 55% of the comparisons (554 out of 612). However, bootstrapping showed a 45% probability that this was just due to random chance. In other words, the effect of RTW on cost-of-living adjusted wages is a toss-up, almost 50-50. So, it seems that the RTW advocates may be right on one thing: States without RTW will have a higher cost of living. The opponents of RTW are also correct: RTW goes hand-in-hand with lower wages. In short, it's a wash. In terms of income including expenses, RTW has no net effect.

All State Differences
Median Wages Adjusted by
Employment, Population, and Cost of Living
Orange: Right-to-work state does better.
Blue: Non-RTW state does better.

Let's Talk Money and Jobs

The tale is not told, though. After all, what if RTW states (like Texas) happen to be very populous states and non-RTW states (like Alaska) are sparsely populated? Then, even though on a pure state-by-state basis, RTW might not do well, in terms of overall prosperity of human beings, it might shine! But how to measure that? If we are thinking primarily of ordinary people—and we should, since the arguments about RTW always get down to whether it helps ordinary people, we can start with median income, again. If everyone were making the median income, the median income would not change. Then multiply the median income by the number of employed people in a state to get an aggregate income estimate. We also have to take into account that a state may have a lot more people to support on top of those who are working. Divide the aggregate income by the state's total population. This "population-adjusted income" can give us an idea of how well each state does vs. another in terms of the comfort of its mass of people.

Let us not forget cost of living, since higher wages are passed on to consumers by the businesses paying them. What does that give us? You've probably already been looking over the last graph. As you can see, RTW does slightly worse than non-RTW in terms of income, adjusted by employment, population, and cost of living. In 292 comparisons, an RTW state did better than a non-RTW state, but in 332 comparisons, a non-RTW state did better than an RTW state. Bootstrapping tells us, though, that this is probably (70%) just random chance. That is, when you get down to the wire, RTW makes no overall difference.

What does this ultimately mean? The claim I tested is "Right to work improves the lot of the worker". In the end, taking into account cost of living, or combined cost of living, employment and population, it's a toss-up. While Right to work might not guarantee misery, it also does nothing to improve the overall condition of the vast majority of Americans. What it tells me, personally, is that Right to Work is a failure. It does not benefit ordinary workers in any way that cannot be just as easily explained by random chance.

What is the take-home? Given the data at hand, a compelling worker-benefit based argument in favor of enacting or maintaining RTW cannot be made. By and large, RTW is not a policy that produces enough benefit to an ordinary worker to be worthy of being kept as law, not even when macro-economic factors such as overall employment are taken into account.

January 12, 2016

Presidential Candidates, Politifact, and Who is Close to Whom

Tree of Candidates, 12 January
image/svg+xml Pelosi O’Malley Johnson Carson Cruz Fiorina Huckabee Clinton Obama Sanders Bush Christie Kasich Paul Rubio Santorum Trump Cluster1 Cluster2 Cluster3 Cluster4

A few months ago, I plotted out the Presidential candidates from the two major parties in terms of their truthfulness. I did this with a "tree" (more of a "bush") diagram based on the Politifact Truth-o-Meter. As I mentioned before, Politifact does provide individual summary charts for each person and a description of the various statements used to create the charts. Unfortunately, comparing profiles isn't straightforward, especially if you want to look at several of them at once. That's where nerdistry comes in.

In addition, a new candidate has formally entered the race since my last attempt. Thus, I again went to the data on each politician's page, ran it through some nerd magic, and came up with a new tree. I restricted myself to formally filed candidates who have more than 4 rulings on Politifact. I also have Barack Obama and Nancy Pelosi, for reference. I color-coded the names by party. You can click on any name to lead you to that person's Politifact page. Four "meaningful" clusters (see below for what "meaningful" means) appeared in the data and have curves drawn around them. The differences among politicians inside the same "meaningful" cluster are not worth noting. Yes, this means that, when it comes to truthfulness, as measured by Politifact, Santorum, Fiorina, Cruz, and Huckabee lump in with Pelosi. Clinton and Sanders (and Obama) are pretty much the same as Bush, Christie, Kasich, Paul, and Rubio.

As last time, the clusters roughly summarize what end of the "True" vs. "Pants-on-Fire" profile a candidate sits on. The top left cluster (Let's call it Clinton-Bush) leans more to "True" and "Mostly True". The cluster on the bottom right (we can call it the Pelosi Cartel, just for giggles) tends to prefer "half true" and "mostly false". The bottom left cluster is heavily dominated by "False", with a dash of "Pants on Fire". O'Malley and Johnson (a Libertarian candidate) are in their own outlying cluster that is more "middling" between true/false. However, both these candidates have relatively few statements in their files.

And the take-home message? Two messages: First, if you agree with Politifact, it's a rough indication of who is more trustworthy. If you reject Politifact's conclusions, just invert the true/false interpretations. Second, you can see who resembles each other in terms of trustworthiness and that this hasn't changed much since August. Agree with or reject Politifact, this part is consistent. Politicians in the same cluster seem to have the same basic character as each other when it comes to honesty or its lack. Like I said, if you dislike Politifact, just flip the interpretation of truth.

Nerd Section

This is a repeat of Agust's methods. I used a copy of "R" statistical language and the "cluster", "gclus", "ape", "clue", "protoclust", "multinomialCI" and "GMD" packages. Then I gathered up the names of declared candidates for US President. I did not intend to limit this to only Republicans or Democrats. Unfortunately, when I looked people up on Politifact, it was only Republicans or Democrats who had more than 4 rulings. Why more than 4? A rough estimate of the "standard error" of count data is the square root of the total. The square root of 4 is 2, which means that if a candidate had 4 rulings, the accuracy was plus or minus 2. Such a large wobble was too much for my taste. This time, I ended up with 17 candidates.

Comparing them required a distance metric. I could have assigned scores to each ruling level and then calculated an average total per ruling. While this might be tempting, it is also wrong. Why is it wrong? Because that method would make a loose cannon the same as a muddled fence-sitter. Imagine a candidate who only tells the complete truth or complete whoppers. If you assign scores and average, this will come out being the same as a candidate who never commits but only makes halfway statements. Such people should show up as distinct in any valid comparison.

Fortunately, there are other ways to handle this question. I decided to use a metric based on the chi distance. Chi distance is based on the square of the difference between two counts divided by the expected value. It's used for comparing pictures, among other uses. However, a raw chi distance depends very much upon the total, and the totals were very different among candidates. The solution to this was easy, of course. I just took the relative counts (count divided by total) for each candidate.

I needed one more element for my metric. Politifact does not rate every single statement someone makes. They pick and choose. Eventually, if they get enough statements, their profiles probably present an accurate picture, but until they get a very large number of statements, there is always some uncertainty. Fortunately, multinomialCI estimates that uncertainty. I ran the counts through multinomialCI and got a set of "errors" for each candidate. I combined these with the chi distances to obtain "uncertainty-corrected distance" between each candidate. Long story short, this was done by dividing the chi distance by the square root of the sums of the squares of the errors. What that meant is that a candidate with a large error (few rulings) was automatically "closer" to every other candidate due to the uncertainty of that candidate's actual position.

I then created a series of hierarchical clustering trees from this set of distances. There is a good deal of argument over which tree creation method is best. I decided to combine multiple methods. I created trees using "nearest neighbor", "complete linkage", "UPGMA", "WPGMA", "Ward's", "Protoclust", and "Flexible Beta" methods. The "clue" package was designed to combine such trees in a rational fashion. Feel free to look it up if you want to follow all the math. I used clue to create the "consensus tree", which is the structure I posted on my blog. But clue doesn't tell you how to "cut" the clusters. For that, I turned to the "elbow method".

The elbow method is an old statistical rule of thumb. Basically, any set of "clustering" has multiple ways you can slice it to say "these things fall into those groups and smaller groups don't really matter". The "elbow method" compares the "variance" of each possible way of cutting the clusters and charts them on the basis of number of clusters vs. "variance explained" by that number of clusters. The math is not simple. What you do is then plot the "variance explained" vs. the number of clusters. What you look for is a "scree" or an "elbow". The line will always be descending. The idea is that you hope there is some point where there is a sharp bend in your line. At the point of that bend is the "elbow". More clusters won't add enough additional explanation to be worth the cut. In this case, my elbow was at four clusters.