A bevy of “right-to-work” laws has been introduced in state legislatures across the United States this year. The legislation has generated intense debate and contention, making headlines across the country. What was most alarming about the parade of bills introduced this year, however, was how their proponents manipulated facts in order to propel them through state legislatures.

As a sociologist who studies unions and someone who relies on good quantitative data, I am bothered most by how the mathematics used to justify these arguments is so deeply flawed–mistakes that any student of statistics could easily spot. Lately I’ve been focusing on the battle over right-to-work legislation in New Mexico, where a bill was dealt a death blow in the state Senate at the final hour.

But workers in other states such as Wisconsin have not fared as well. In March, the Midwestern state became the 25th in the US to prohibit unions from negotiating contracts that require union and nonunion employees to pay their share of costs for all the benefits the union provides.

The results of this war on workers may vary from state to state, but the genesis of these salvos and the misleading arguments used to muscle them through legislatures are the same. A careful analysis reveals their scientific and intellectual flaws.

Boiler-plate blueprint

The legislation that failed to pass in New Mexico was eerily similar to boiler-plate language that conservative organizations such as the National Right to Work Committee and the American Legislative Exchange Council (ALEC) have been circulating through regional lobbying organizations that are typically part of the conservative State Policy Network.

In New Mexico, that organization is the Rio Grande Foundation. Its president, Paul Gessing, has argued in various news outlets and in testimony to legislators that right-to-work laws increase economic growth, jobs and personal income.

The problem? As I’ve noted elsewhere when challenging Gessing’s arguments, he and others have based these assertions not on scientific evidence but on the faulty math of failing to control for the multitude of factors that contribute to economic growth.

The problem with the misuse of math is illustrated plainly by the well-worn storks and babies example. Numerous studies have found a correlation between an increase in the stork population and a rise in human birth rates. Of course, we know storks don’t deliver babies, and once we control for other factors that create this seemingly causal relationship it disappears entirely–as is the case with the false relationship between right-to-work laws and economic and job growth.

Lower wages

In fact, the scientific research actually shows the opposite of what right-to-work proponents have claimed.

The most rigorous research study available–published in 2011 by the nonpartisan Economic Policy Institute and conducted by Heidi Shierholz (now the chief economist of the US Department of Labor) and Elise Gould–controlled for 42 variables. It found that right-to-work laws result in lower wages and a lower likelihood of health care and pensions for union and non-union workers. It also shows right-to-work laws have no impact on economic growth.

Right-to-work proponents, however, have used “research” reports that control for few if any variables, to suggest that right-to-work states have done better on a variety of growth measures, predicting that their state would similarly benefit by passing a bill.

For example, the Wisconsin Public Research Institute, a member of the free-market-oriented State Policy Network, published such a report before the state passed its law that claimed that adopting right-to-work could increase per-capita income by 6 percentage points. But the study only controlled for eight variables, which isn’t nearly enough to control for all the different factors that affect changes in income.

In other words, the conclusions are meaningless. In the world of medical research, this would be like testing a cancer drug without using a control group that was not given the drug, ensuring that its pure effect could be isolated.

Another problem with right-to-work proponents’ math is that making predictive arguments using simple averages of other states’ growth rates makes no sense statistically.

It’s comparable to the argument that on average people with larger shoe sizes are more likely to have heart attacks. Does this mean shoe size predicts heart attacks? No, there are other variables that are having effects such as age – since children are much less likely to have heart attacks.

Only regression analysis allows us to isolate the effects of a key variable (storks, shoe size, right-to-work laws) on a given outcome and eliminate the effects of others. The problem with making predictions based on simple averages is easy to see when we examine right-to-work proponents’ favorite case–Oklahoma.

Misusing anecdotal evidence

Gessing told New Mexico lawmakers that Oklahoma’s economic growth is the result of its 2001 right-to-work law. But he failed to mention that over the same period Oklahoma’s economy was benefiting from rising prices for oil and natural gas – and more recently from higher levels of production–factors that would make a significant contribution to growth.

Gessing also argues that there are “reams of data” showing right-to-work states create more jobs, which is not true. He didn’t note, for example, that manufacturing employment in Oklahoma fell sharply in the first three years after the state passed its law in 2001 and is currently down about 22% since then.

So in the case of Oklahoma, what was likely actually happening? Oil and natural gas made rich people richer through their investments, lifting per-capita personal income but not average worker wages.

It is unlikely that right-to-work laws had any impact on Oklahoma’s economic growth. Nor is there convincing evidence that they had an impact on job growth in Michigan and Indiana, as proponents similarly have tried to argue using averages, falling into the shoe size-heart attack trap.

RTW laws fail to lure business

Across the country proponents have also argued that right-to-work laws would put their states into consideration for more private sector jobs, a claim for which I cannot find any scientific evidence at all in any state. Instead, they rely on anecdotal examples to make their case.

And ultimately, stories about what employers may or may not do in the future if a state were to pass a right-to-work law does not constitute scientific data; there are so many other factors that affect business decisions about where to open a factory or office. Scientific research on the location decisions of US and foreign corporations suggests that among the most important variables are: market size, local taxes, wage rates and transportation infrastructure – but not right-to-work laws.

In the 2014 State New Economy Index, which compares states every year for their attractiveness to high-tech, high-wage manufacturers, none of the top five states were right-to-work states, and only two of the top 15 were. What were the companies surveyed looking for? Perhaps surprisingly, they were not looking for cheap labor but rather for states with good education systems, good research universities and skilled workers who would stay for a long time.

What really drives an economy

The debate about right-to-work laws across the country this legislative session has misdirected our collective focus and energy away from what solid evidence suggests will improve states’ economic futures: creating a solid infrastructure, equipping our schools and teachers with resources and seeking out emerging and innovative industries that offer better and more permanent jobs.

Scientific research also suggests that improving wages and reducing inequality across the US depends on the existence of strong unions.

Although right-to-work laws are proffered as part of a state’s economic development strategy, their real goal is to undermine workers’ collective voice and power.