## 2019

STATISTICS ROUNDTABLE

# Salami Slicing

by Lynne B. Hare

He uses statistics as a drunk uses a street lamp, for support rather than illumination.–– ANDREW LANG

Stop me if you’ve heard this before. No, don’t. Many hear; few listen.

Sam Shaker, salami maker, labored under a financial crunch. Salami sales slumped—protein was in, but fat was sin. Desperate to keep a happy face turned toward Wall Street and knowing consumers would never accept another price increase, Sam’s solution was to slice the salami. That’s the part you may have heard before.

Sam wondered how thin he should slice the salami. Oh sure, he could do the math to compute dollars per thickness of slice, but could he get away with the deception of selling less salami per dollar? “Of course,” said the little devil on Sam’s shoulder. “Save that slight slice and take it to the bank. No one will be the wiser. Haven’t I always advised you well in the past?”

Well, you can never have enough devils, so Sam hired a statistician, but not just any statistician. He hired a sleazy, sniveling statistician who suggested Sam launch a survey to see whether customers could tell the difference between Sam’s standard salami and the salami shortened by a slight slice sufficiently sizable to satisfy the Street.

The statistician then taught Sam about the Greeks. Alpha is the chance your sampling of the salami consuming population will cause you to conclude the missing slice will be detected when it actually makes no difference. Beta is the chance your sampling will cause you to conclude the missing slice won’t be detected when, in fact, it will. Delta is the size of the attitudinal or preferential difference you think might make a difference to your sales, and sigma is the sampling variation.

Sam was not so sure about all that, but he figured it was better to go with the devils he knew than those he didn’t. Sam ran the test, found no difference, took a slice off his salami, saved a buck and, the next year, found himself in the same situation—wondering what he was going to do to please the Street.

Sam’s statistician won the lottery and retired to Stintino in southern Sardinia. Sam wanted to slice some more, but he couldn’t fathom the Greeks, so he hired another statistician.

The new statistician, upon hearing of his predecessor’s fate, assured Sam he would be available to serve for the foreseeable future and told him the lottery was a tax on people who were bad at statistics. Sam was baffled by such logic but decided to work with the statistician anyway. “Don’t slice the salami anymore,” he told Sam.

Crestfallen, Sam wondered what he could do instead. “Innovate,” said the statistician. “No one ever made a buck slicing the salami. Not in the long run. Not really.”

“But my previous test said it was OK,” cried Sam.

“Your previous test said the difference was under the detection limits. It’s like flying under the radar,” said the statistician. “Where did you get your salami recipe?”

Proudly, Sam said, “It’s been handed down from Shaker to Shaker for many generations, all the way back to Schwetzingen, home of the annual asparagus festival.”

“Have you ever thought of making it better?” asked the statistician.

“Look,” said Sam, “I’m trying to save money, not spend it.”

Sam was about to dismiss this statistician, buy lottery tickets, take another slice off the salami and let the devil take the hindmost when the statistician said, “Me, too. There’s nothing optimal about your current recipe. It began as a farm kitchen recipe and was then tweaked to fit the equipment in your factory, right?”

Sam nodded.

“Then why not look at your salami composition for opportunities to reformulate to consumer tastes?” continued the statistician. “You might just find something consumers like more that costs you less to make.”

Sam was skeptical but wanted to give it a try nonetheless. He and the statistician designed a study in which the salami ingredients Sam thought would influence consumer attitudes were varied systematically.

Until that point, Sam thought he knew everything there was to know about salami. But as a result of the study, he learned some salami ingredients raised acceptance but should not be present in the mix at the same time. Others seemed to serve no value even though they were expensive.

Sam’s new formulations helped him turn a tidy profit, kept the Street off his back and taught him why the old method was called salami slicing.

The moral of the story: Seek statistical support to optimize, not slice.

LYNNE B. HARE is program director of applied statistics at Kraft Foods Research in East Hanover, NJ. He received a doctorate in statistics from Rutgers University, New Brunswick, NJ. Hare is a past chairman of ASQ’s Statistics Division and an ASQ Fellow.

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