One month out of each semester, we GSIs must pay union dues or a service representation fee to our union, the Graduate Employees’ Organization. I had forgotten that March is one of those months, and I had an interesting discussion with myself as I looked at my last paystub and found that because of union dues, my check was less than I had expected.

Matthew Zabka

On one hand, I don’t like being forced to give the GEO money, which it then uses to fight for causes with which I don’t agree. On the other hand, if workers were not forced to pay dues to the union that represents them, there could be an incentive for those workers to free ride — meaning a worker could expect union perks while not contributing his or her fair share for such benefits.

Unlike most discussions I have with myself, this one is also taking place across the country. Republicans in several states such as Michigan have mulled over introducing right-to-work legislation that would ban requiring union dues as a condition of employment. While both sides of the right-to-work issue have reasonable claims, and debating right-to-work laws is important for society, politicians and the media have, as usual, reduced a worthy policy debate to bad rhetoric and an even worse use of statistics.

The rhetoric includes some who have mockingly branded right-to-work laws as “right to work for less” laws. They claim that the laws weaken unions, which in turn lead to reduced wages.

One user of such rhetoric, Prof. David Schultz of the School of Business at Hamline University in Minneapolis, Minn., has attempted to justify this claim using statistics. Before looking at Schultz’s reasoning, one must understand what the statistical term correlation means and what it tells us.

Correlation is a number between -1 and 1 that measures the strength of an association between two sets of data that are collected for the same individuals. A correlation close to -1 or 1 suggests a strong association, while a correlation closer to 0 suggests a weak association.

If a correlation is positive, one expects points of the two sets of data to increase together. For example, if one looks at the heights and weights of individuals, one would expect a positive correlation, since taller people tend to be heavier than shorter people.

If a correlation is negative, one expects points of one set of data to decrease as points of the other increase. One might expect a negative correlation between students’ time spent on Facebook and students’ GPAs. Time spent on Facebook is time not spent studying, so increased time on Facebook may be associated with a lower GPA.

Back to right-to-work laws. Schultz measured the correlation between right-to-work laws in states and median family income. He found a weak, negative correlation of -0.40. This means that on average, states with right-to-work laws tend to have lower median family incomes. Schultz then concluded from his analysis that, “right-to-work laws depress family incomes.”

His conclusion is wrong and serves as a depressing example of how statistics are misunderstood or twisted to support a political agenda. Correlation only measures an association between two variables. It tells us nothing about one variable causing the other.

The number of boating accidents per week and the number of ice cream cones sold per week are positively correlated, but boating accidents do not cause people to buy ice cream, and ice cream probably doesn’t cause many boating accidents. Instead, both of these things happen to increase together in warmer weeks.

Just as weather is lurking behind the association between ice cream sales and boating accidents, several other variables could be lurking behind the negative correlation between right-to-work laws and median income. Education levels, proportion of stay-at-home parents, geographical location and countless other factors could be the real causes of the lower mean median incomes in right-to-work states.

The debate over right-to-work laws is important for society to have, but this debate should be grounded in solid reasoning instead of heated rhetoric and bad statistics. I have my own opinions on right-to-work, but I have no idea if such laws cause lower median incomes, and neither does Schultz.

Matthew Zabka can be reached at mzbka@umich.edu. Follow him on Twitter at @MatthewZabka.