ceguiera

statistical illiteracy

statistics gets a bad name the same way that bologna does. an unscrupulous or incompetent person makes use of it, then everyone who sees the parody version rejects the genuine article.

consider this paragraph from the NYTimes opinion page:

This is a divide that goes deeper than economics into the way people perceive the world. If you show an American an image of a fish tank, the American will usually describe the biggest fish in the tank and what it is doing. If you ask a Chinese person to describe a fish tank, the Chinese will usually describe the context in which the fish swim.

the inference that the columnist makes here is quite absurd. he wishes us to imagine a chinese person and an american person, each of whom looks at an image of a fish tank numerous times. the american talks about the biggest fish the first time, the second time, the third time, and the fifth time, but decides to talk about the context in which the fish swim on the fourth time. the chinese, mutatis mutandis, does something similar.

the columnist probably meant to say:

This is a divide that goes deeper than economics into the way people perceive the world. If you show a large group of Americans an image of a fish tank, most of them will describe the biggest fish in the tank and what it is doing. If you ask a large group Chinese people to describe a fish tank, most of the Chinese will describe the context in which the fish swim.

the columnist seems indifferent about the difference between comparisons of different people at one instant in time and comparisons of a single person with its past or future self.

let a defender of the columnist object "but that's what he meant anyways, why be so picky?" i'll be picky for the benefit of all statistically-derived arguments.

in the present published wording, i could easily refute the columnist's assertion by finding a single chinese person, to whom i showed a picture of a fish tank, who described to me the biggest fish. to refute the paragraph written as i have suggested, i would need to find a suitably large group of chinese people, the majority of whom describe the big fish.

perfectly reasonable assertions are vitiated in the minds of people who fail to distinguish as the columnist did.

e.g. Garnus, having conducted a study (n=350) says: "Sinhalese women have a natural beauty."
Argos hears: "A Sinhalese woman, most of the time, has a natural beauty," then responds "That is not true. My oncologist is Sinhalese and she plasters on makeup like a trollop."

or more commonly, a generalization is drawn without evidence.

e.g. Argos, lusting after his Sinhalese oncologist, says, "Most of the time, this Sinhalese woman, plastering on makeup like a trollop, excites me." Garnus hears: "Most Sinhalese women, plastering on makeup like trollops, excite Argos," and decides not to enroll his son in the much-acclaimed Sinhalese private school.

this fallacy is usefully employed in self-defense.

e.g.
Argos: "Garnus, you've been drinking so much since your bankruptcy."
Garnus: "No, you should see some of the drunks at the bar, now that's who you should worry about."