Understand False Positives to Better Grasp the Real Thing

Object of  suspicion*

Five days after the outrage in Paris, an early-evening phone call to police in Northampton, Massachusetts spurred the evacuation of 25 residents from a Main Street building and surrounding businesses. The caller was wary of a mysterious plastic-wrapped box on a ledge above the front doorway of Casa Del Sol, which sells imported clothing and crafts. (The shop had closed for the day two hours earlier.)

The police and fire departments, which deemed the object “suspicious,” brought in members of the Massachusetts Bomb Squad, who determined that the box was a small speaker. “We always like to play a little bit of music,” Casa Del Sol owner Edmundo Becdac later told The Daily Hampshire Gazette. He had wrapped the speaker in plastic to protect it from late autumn dust.  The speaker, he noted, had generated tunes from that same perch day in and day out since the store’s opening day—ten years ago.

The object of suspicion back in commission four days later

False Positive Fandango

“Terrorism breeds false positives,” laments a friend who teaches statistics. When introducing his students to false positives, i.e., Type 1 errors, he cites mammogram studies. If your mammogram tests positive, your chances of having breast cancer may be significantly lower than you think.

A mammogram will yield a true positive 90% of the time if you do have cancer. But if you don’t, you still have a 7% chance of registering a false positive. Because that population dwarfs its counterpart, false positives among cancer-free women drastically skew the overall results. When you account for that distortion, only 9% of women who test positive from mammograms should expect to have cancer. The moral of the story: If your mammogram comes up positive, retake the test (maybe more than once) before electing biopsies, surgery, and chemotherapy.

Confirmation Insinuation

The Northampton incident and other false positives frequently fall prey to what psychologists call the confirmation bias. You see a mysterious box over a doorway, so you suspect the worst, cherry picking whatever confirmatory evidence you can muster in its support while ignoring anything that contradicts it. For a best-in-class example by a public official, revisit Colin Powell’s wishful public interpretation of the photographic evidence alleging Sadam Hussein’s weapons of mass destruction. 

Graphic from Gen. Powell's tragic fool's errand

Two Who Cried Wolf
 
“Crying wolf” is another variation on false positives.  Pioneering social scientist Stanley Milgram and comedian Red Foxx cried wolf once too often. Much of Milgram’s research involved conning his subjects, including the dupes in his bogus “shock machine” experiments of 1962/63. Can you blame a lecture hall of students for doubting him when he burst into a fellow professor’s lecture, yelling, “I have horrible news. President Kennedy has been shot in Dallas.”? Barry Wellman, who became a professional sociologist, remembers blurting out:"You're just doing another experiment on us."

In the 1970s TV series Sanford and Son, most episodes featured Redd Foxx’s character, Fred Sanford, clutching his chest and crowing to his long-suffering son, Lamont, “Oh! It’s the big one; Elizabeth [Fred’s deceased wife], I’m coming to join you, honey!” Years later (1991), when the actor collapsed at a rehearsal on the set of the CBS television series, The Royal Family, his costar Della Reese and other cast members suspected that he was treating them to his signature routine. But they soon realized the truth: Mr. Foxx was down for the count at age 68. More on Milgram and Foxx here.

*Dan Little--Daily Hampshire Gazette