Southern and Northern Democrats considered together did not at all resemble Northern or Southern Democrats considered separately. The lurking variable was the importance of regional attitudes at a time that Jim Crow was being challenged and dismantled. Constituencies in the South were far more hostile to the Act than constituencies elsewhere.

Variables Lurking Everywhere

The other stories from our list also all suffer from lurking variables.

At Berkeley, it turned out that women and men applied to different programs and departments within the Graduate Division. Women gravitated toward programs with fewer available positions and lower acceptance rates, while men gravitated toward programs with higher acceptance rates. Since applications were handled on a departmental basis, the lurking variable is the department students applied to.

During the 2016 election, voters earning less than $50,000 a year did indeed favor Hillary because voters in that bucket are disproportionately represented by ethnic minorities who typically vote Democrat. White working-class voters favored Trump more strongly than they did previous Republican candidates — enough to swing several battleground states. Race (and, potentially, urbanicity) is the lurking variable in this case.

In the case of kidney stone treatments, it turns out that less-invasive surgeries were performed on less severe cases of kidney stones, explaining the higher success rate. The lurking variable, in this case, is the severity of the ailment.

The median income in the United States continues to rise even as income for people at every level of education declines because a much higher proportion of people now have bachelor’s degrees. The lurking variable here is the change in time of the proportions of people with different levels of education.

Reaching the Right Conclusions

For practical business purposes, plenty of dimensions can function as lurking variables. Local and international users might be present in different proportions and respond differently to certain products or marketing initiatives. Your pool of lower-margin customers might grow at a different rate than your pool of higher-margin customers.

All of these can produce seemingly conflicting measurements and deserve careful investigation. Measuring the right things is hard, and you don’t want to leave figurative stones unturned. As a rule of thumb, numbers must be analyzed at deeper than face value. The sniff test is whether you have accounted for all obvious outside influences, and above all whether you can construct a coherent story about how these measurements came about.

P.S. Don’t panic, but double (and even n-tuple) Simpson’s Paradoxes are possible, too!