James Sherk of the Heritage Foundation explains for National Review Online readers the flaws in the argument that a $15 minimum wage would raise fast-food prices by just 4 percent.

If something seems too good to be true, it probably is. Unfortunately, many journalists did not remember that when covering a new report claiming $15-an-hour wages would raise fast-food prices only 4 percent.

A closer look shows that the study underlying the report had major methodological errors. More serious analysis shows that $15-an-hour wages would raise fast-food prices by over a third — at least until stores automate work currently done by humans.

The study, by Purdue University economists Richard Ghiselli and Jing Ma, has made quite a splash. The Washington Post covered it extensively, concluding that the higher wages for fast-food workers would add just 17 cents to the cost of a Big Mac. Local papers have covered it too. ThinkProgress argued that the study undercuts arguments against $15-an-hour fast-food wages. If the study were accurate, it would be hard to argue with them.

However, Purdue’s report offers a case study in why journalists should consult multiple sources before going to press. Simple back-of-the-envelope calculations show that the Purdue results are impossible.

Labor accounts for a quarter to a third of the average fast-food restaurant’s costs. Currently, wages in the fast-food industry run around $9 an hour. Going to $15 an hour means increasing pay by over 50 percent. Prices would have to rise by at least one-sixth (50 percent multiplied by one third) to cover the base-wage increases. Of course, those price increases would drive some customers away, so restaurants would need to raise prices again. But as a baseline, prices would have to rise by at least one-sixth.

The Purdue study finds price increases an order of magnitude smaller. It does so by making a basic math error. The Purdue researchers got their data from the National Restaurant Association’s (NRA) 2014 operations report. The report surveys restaurants and shows how much the median restaurant spends on various expenses, such as payroll, food, marketing, etc. The Purdue researchers added those figures to derive the balance sheet of the typical fast-food restaurant.

Mathematically, however, medians do not work that way. Average values will add to the overall sum, but medians typically do not. The preface of the NRA Operations Report emphasizes in highlighted text that researchers cannot add median values to get overall expenses. Nonetheless the Purdue researchers did exactly that.