How to Lie with Statistics

a difference is a difference only if it makes a difference.

It ain’t so much the things we don’t know that get us in trouble. It’s the things we know that ain’t so. —Artemus Ward

A well-wrapped statistic is better than Hitler’s “big lie” it misleads, yet it cannot be pinned on you.

IF YOU can’t prove what you want to prove, demonstrate something else and pretend that they are the same thing. In the daze that follows the collision of statistics with the human mind, hardly anybody will notice the difference. The semiattached figure is a device guaranteed to stand you in good stead. It always has.

Just to clear the air, let's note first of all that whatever an intelligence test measures it is not quite the same thing as we usually mean by intelligence. It neglects such important things as leadership and creative imagination. It takes no account of social judgement or musical or artistic or other aptitudes, to say nothing of such personality matters as diligence and emotional balance.

Extrapolations are useful, particularly in that form of soothsaying called forecasting trends. But in looking at the figures or charts made from them, it is necessary to remember one thing constantly: The trend-to-now may be a fact, but the future trend represents no more than an educated guess. Implicit in it is "everything else being equal" and "present trends continuing." And somehow everything else refuses to remain equal, else life would be dull indeed.

proper treatment will cure a cold in seven days, but left to itself a cold will hang on for a week.

The purely random sample is the only kind that can be examined with confidence by means of statistical theory, but there is one things wrong with it. It is so difficult and expensive to obtain for many uses that sheer cost eliminates it. A more economical substitute, which is almost universally used in such fields as opinion polling and market research, is called stratified random sampling.

Hardly anybody is exactly normal in any way, just as one hundred tossed pennies will rarely come up exactly fifty heads and fifty tails.

The purely random sample is the only kind that can be examined with entire confidence by means of statistical theory, but there is one thing wrong with it. It is so difficult and expensive to obtain for many uses that sheer cost eliminates it. A more economical substitute, which is almost universally used in such fields as opinion polling and market research, is called stratified random sampling.

How results that are not indicative of anything can be produced by pure chance—given a small enough number of cases—is something you can test for yourself at small cost. Just start tossing a penny. How often will it come up heads? Half the time of course. Everyone knows that. Well, let’s check that and see…. I have just tried ten tosses and got heads eight times, which proves that pennies come up heads eighty percent of the time.

The secret language of statistics, so appealing in a fact-minded culture, is employed to sensationalize, inflate, confuse, and oversimplify.

There are at least three levels of sampling involved. Dr. Kinsey’s samples of the population (one level) are far from random ones and may not be particularly representative, but they are enormous samples by comparison with anything done in his field before and his figures must be accepted as revealing and important if not necessarily on the nose. It is possibly more important to remember that any questionnaire is only a sample (another level) of the possible questions and that the answer the lady gives is no more than a sample (third level) of her attitudes and experiences on each question.

My trick was to use a different kind of average each time, the word "average" having a very loose meaning. It is a trick commonly used, sometimes in innocence but often in guilt, by fellows wishing to influence public opinion or sell advertising space. When you are told that something is the average you still don't know very much about it unless you can find out which of the common kinds of average it is- mean, median, or mode.

Permitting statistical treatment and the hypnotic presence of numbers and decimal points to befog causal relationships is little better than superstition.

To be worth much, a report based on sampling must use a representative sample, which is one from which every source of bias has been removed. That is where our Yale figure shows its worthlessness. It is also where a great many of the things you can read in newspapers and magazines reveal their inherent lack of meaning.

It is dangerous to mention any subject having high emotional content without hastily saying where you are for or agin it.

The fault is in the filtering-down process from the researcher through the sensational or ill-informed writer to the reader who fails to miss the figures that have disappeared in the process. A good deal of the misunderstanding can be avoided if to the "norm" or average is added an indication of the range. Parents seeing that their youngsters fall within the normal range will quit worrying about small and meaningless differences. Hardly anybody is exactly normal in any way, just as one hundred tossed pennies will rarely come up exactly fifty heads and fifty tails.

My trick was to use a different kind of average each time, the word “average” having a very loose meaning. It is a trick commonly used, sometimes in innocence but often in guilt, by fellows wishing to influence public opinion or sell advertising space. When you are told that something is an average you still don’t know very much about it unless you can find out which of the common kinds of average it is—mean, median, or mode.

What comes full of virtue from the statistician’s desk may find itself twisted, exaggerated, oversimplified, and distorted-through-selection by salesman, public-relations expert, journalist, or advertising copywriter.

As Henry G. Felsen, a humorist and no medical authority, pointed out quite a while ago, proper treatment will cure a cold in seven days, but left to itself a cold will hang on for a week.

graphs are not always what they seem. There may be more in them than meets the eye, and there may be a good deal less.