The Whole Is Less Than the Sum of Its Parts

There are over 1,000 separate tables in the U.S. Statistical Abstract covering nearly every imaginable statistical measurement of our society from birth rate to lumber consumption. But there are only four tables that measure social disintegration. Prisons and prisoners are reported, but the ratio of false arrests to convictions is not measured; the level of toxic wastes, the corporate crimes, and the countless individual encounters with small claims courts aren't; nor are most of the other serious snafus in life.

We measure what makes us look good. Not only is measurement like other communication&emdash;reflective of the collector's point of view&emdash;but statistics in its broadest sense is designed to support a narrow perception of the world. It is my contention that the common perception of the world, which is based on a long chain of daily reasoning including statistical logic, is inappropriate.

The Outsider's View

We start with Alfred Kinsey, one of my heroes, not only because his Sexual Behavior in the Human Male was the first accurate statement about sexual behavior in human history, and because he died as a result of his own integrity, but because he was a fool in the most profound meaning of that word. The story is well told by Wardell Pomeroy in his biography of Kinsey. I read Kinsey's book on male sexuality at the age of 14 and was stunned by his candor, and grateful. He answered questions I had given up asking several years earlier.

Kinsey started his research in the 1930s when, as a preeminent zoologist, he was asked to teach an undergraduate course on marriage and sex. He found that nothing significant had been published on the subject. Far more was known about moth and butterfly sexual behavior than about that of humans. So, honest man that he was, he set about collecting the data. A comparable study of the U.S. population was not again undertaken for 38 years.

The only reason Kinsey brought this information to our attention is that his scientific training led him to seek information about humans as though we were an animal species. He lacked the common man's understanding of social systems that would have kept him from doing his research in the first place.

In the mid 1950s, after publishing his second volume, on female sexuality, he was bewildered at the anger and viciousness that was directed at him. Attacks came from everywhere, including Congress and the very foundations that had paid for the research. (Kinsey didn't live long after this assault; he died young, heartbroken.)

Kinsey showed what knowledge was possible if we were just able to break our shackles of "reasonableness" and be foolish enough to collect it.

Most information that I have found relevant to understanding our world is not collected. Social science research, like all research, is actually done in support of the current conceptual structures. (See W.E. Bijker, Hughes, Pinch,The Social Constructions of Technological Systems, MIT Press, 1987.)

A Story About Court

In a court hearing where I was being cross-examined about my qualifications as an expert witness, the opposing lawyer pulled out a book I had written, The Seven Laws of Money, and found this quote: 'The realm of logic in Western man comprises about 2 percent of his reality.' "Could a person who wrote that give useful expert testimony?" he asked.

I answered: "Let me prove the point. In this courtroom, where dozens of people are coming and going every hour, we have no measurements or records of their movements, interactions, dress, states of mind, or behavior. Yet that little device on the wall (a thermostat) is paying close attention to the movement of air molecules in the room and even controlling them. That device represents the 2 percent of the rationality in this room."

Another Story: About Teaching Statistics

I had a startling experience in 1960 when I was a teaching assistant in statistics and chose to use the Surgeon General's Report on Smoking and Cancer (the first one) as the source of three tables for a homework assignment.

The night before the assigned class date, I sat down to do the homework myself, with the slide rule we used in those days. The next day, I was not surprised to find what the students who had done their homework confronting me.

The assignment included a Chi-square test on one table that listed urban/rural at the top and smoker/non-smoker on the side; inside the table were the death rates from lung cancer. (Chi-square, like most statistical tests, examines variance. Variance is what you perceive in the following two sets of numbers: 2-5-3-6-2 and 5-63-48-91-12. The former has less variance.)

The Surgeon General's table, when statistically tested, contrary to statements in the text, showed that smokers in the country had less risk of lung cancer than nonsmokers in the city. It was not an indictment of smoking by any stretch of the imagination.

The second table to be statistically tested by the students in the class was the Causes of Death of Smokers, ranked from 1 to 15 in one column with the same rates for nonsmokers in an adjacent column. The test the class was to use is called Students' t Test. This test also compares variance. Again the results were that smoking was not a significant factor in the causes of death.

Reading the table as statisticians, we found that smoking couldn't be blamed for all the ills listed. In the top fifteen ills among smokers, along with lung cancer and heart disease, were testicular cancer and suicide. Smoking appeared to be related to some other attribute, say attribute X, and X meant early death for people who had that attribute. X'ers obviously love to smoke. To this day, X is unknown, and 30 years later, a reasonable test has not yet been done on attribute X evidence.

Fortunately for me as a teaching assistant, the third table compared smokers and non-smokers on emphysema. When the students did their calculations correctly they found a strikingly high, statistically significant rate of emphysema among smokers.

The class discussed the findings and concluded that for the past 300 years the pleasures of tobacco were disdained by Puritans and that puritanism had finally enlisted science and medicine to prove its moral point.

Call the Press

I phoned the local newspaper science writer and sent him our findings. He wrote a banal article pointing out that the blue-ribbon commission didn't have a statistician on it. The next Surgeon General's report had a statistician on the panel and the two tables we had tested and found wanting were dropped.

Statistical Testing

Good statistical tests are very useful when applied to appropriate data. The role of the statistician on the Surgeon General's task force, however, was to eliminate inappropriate tables and not rock the boat.

Statisticians, even today, forty years after statistics became a required course in the social sciences, seldom see the basic tables to which such tests can be appropriately applied. In fact, good statistical tests are so promiscuously misused in our society, particularly in psychology and medicine, that the word promiscuous should be restricted in its usage to this narrow subject rather than to sexual behavior.

The Baby and the Bath Water

Statistical tests warrant my respect because I have used them for decades with useful results. However, the science of statistics is based on two principal concepts: variance, which I will call the baby, and probability, which is the bath water.

Variance and variance measurements are derived from a phenomenon that is called The Law of Large Numbers; it is also referred to as the Bell Curve, or Gauss Distribution. It seems to be a quality inherent in the nature of human measurement, as almost anything we set out to measure ends up reflecting the Law of Large Numbers.

Suppose we picked up pebbles on the beach and every five feet we filled a paper bag with them. We might deliberately mix large pebbles with small ones in order to get extremes in sizes in various bags. When we finally measured what we had done, we would find that the variance in individual bags was much greater than the variation in the whole pile of pebbles when poured on the table together. This is an example of the Law of Large Numbers.

I mentioned humans creating the law of large numbers above. Had a young child filled each bag, some bags would be full others would be nearly empty still others might have sand in them. The Law of Large Numbers wouldn't work.

The world so consistently reflects this phenomenon when we (adults) measure it that it makes statistics a powerful tool. It's the real baby of statistics underlying most statistical tests, including linear regression and correlation analysis.


Variance seems a very reasonable and comforting concept to me, while probability, as used in every aspect of our lives, doesn't. The probability of getting a 3 on the throw of a die is 1/6th, two 3's in a row 1/36th. The probability of drawing two pairs in any one hand in a poker game is 1/6th. The underlying logic, the overlying logic, and the only logic in these instances is that each throw of the die or draw of the cards is independent of the last act. It is assumed that the die is a perfect shape and the cards are well shuffled after each hand&emdash;more than seven shuffles of the cards is statistically sufficient.

Independence is a strong concept on which modern probability rests, or sleeps, to be more precise. It means that each separate event is in every way unrelated causally, theoretically, and even spiritually, from the previous event. There is no probability of nonindependent events. Every statistician reading this knows that. If events are not independent, then the appropriate discipline to apply is sociology, physics, or philosophy. Probability and independence are as mutual as a hand and fingers.

The Widespread Use of Probability

Like doctors who used to keep the diagnosis of terminal cancer from their patients, we are never reminded in the countless probabilistic statements we hear daily that probability is only meaningful when events are independent. Furthermore, independent events in human life are so rare as to be nearly nonexistent outside of gambling tables and sporting matches.

We are typically told that the probability of rain today is 30 percent. This probability is derived from looking at the frequency of rain in the past on this specific date when comparable weather conditions prevailed&emdash;such as falling barometric pressure and a low pressure front within 300 miles. (this was written before satellite photos of weather were common.) Unfortunately, weather is a highly interdependent system in which the previous day's and the next day's circumstances are closely related. The use of probability in relation to weather phenomena is totally inappropriate.

As evidence, consider two days in a row where the weatherperson forecasts a 30 percent chance of rain. If probability applied, we could say that the chance of two days rain in a row would be 9 percent. But that is wrong because of a phenomenon known as the seasons, which bring much more rain at some times and less at others. And rain often occurs for days at a time. In some cities, it occurs most of the time.

Highly Improbable

The probability that the person next to you on an airplane was born in this month is approximately 1/12th. But the reality is different, because many people travel on a date near their birthday. Don't make bets where social sorting processes are going on.

Virtually all human activities are highly interrelated. Our sense of probability as commonly used overlooks this. Two encounters in Tokyo make this point. One was with Barbara, a woman I hadn't seen in five years and ran into at the Imperial Hotel. She was startled and amazed. What incredible odds against this happening! "Synchronisity," she exclaimed.

Not really. Most traveling Americans in my social network choose among very few hotels if they come to Tokyo for their first trip. The Imperial is one of them. In addition, I was a little homesick that day and stopped to have a drink in the lobby and sat where I could see the lobby traffic. Westerners stand out very readily in Japan. So the odds of my finding someone I know were high after all.

I met Franz while walking down the street near a large modern hotel in the Shinjuku area in the afternoon, eliciting total incredulity on his part. The encounter was not too surprising to me, however. I suspected he would be in Tokyo within a few weeks of me; from comments through the grapevine, I knew he would be on a speaking trip paid for by wealthy Japanese patrons, and I kept my eyes open whenever I was near a place where he was likely to be. Moreover, on reflection I realized we had the same travel agent, that we were probably put on the same discount airplane flights, and that we were likely to be invited to mutual friends' offices and parties while in town. So I was, in fact, very likely to see Franz in Japan; only the exact site was uncertain.

These are minor examples to make the point that social interconnections and social sorting account for most human interactions and coincidences. Synchronisity is not a good description for many of the events in our lives, as it presumes low probability and that in turn presumes independence.

The World of Probability Is Even Smaller

Most of the events in our lives are concerned with human interaction or human interaction with human-designed artifacts, which is a pseudo human interaction. Virtually nothing is functionally, practically, or meaningfully independent except games with independence designed into them.

People are astounded when a machine works after being hit with a hammer, when the car starts again after it has just stopped for no reason, when three things on the motorcycle go wrong at the same time, and when you pick up the phone and the person you were going to phone is on the line. But artifacts are not only consciously designed to fit into human systems, they have strong evolutionary components in their design that reflect human behavioral qualities. Hitting a machines is a learned response in humans, and machine self-correction and failure systems are deliberately designed with this in mind.

The three-way-collapse phenomenon, particularly familiar in American machines, is part of an unspoken engineering tradition. In fact, all nations have specific engineering patterns. This is evident in the English automobile, where the electrical systems are unrepairable. French equipment failures are always in inaccessible locations, Russian equipment is klunky and heavy but very durable, and American equipment is known abroad for "one-horse-shay" collapses (everything goes at one time).

As for the occasional coincidence when picking up the telephone, this machine could have been designed so that an incoming call can't be heard until the receiver's bell rings, but the designers welcomed the serendipitous error when they first found it in their early phone systems.

Robust Data

Having cheered for statistical analysis based on variance and booed deductions based on probability (which of course includes correlation analysis, a widely recognized theoretical swamp), let us examine one more statistically related research story. It began with a lawsuit against the phone company, which had unleashed a horde of salespeople to sell phone services such as call forwarding, call waiting, and speed dialing. The salespeople quickly found that customers who couldn't speak English also couldn't complain very effectively about unknown fees being added to their monthly phone bill. For the salesperson to get prizes and bonus awards for sign-ups, it was easy to sign up any voice they heard that didn't speak English. As a result, migratory farm workers, earning $16 a day, were frequently found to have all these new business-related services on their phone bills.

In remedying the situation, it was necessary to conduct interview surveys to determine the extent of the marketing abuse. The phone company hired a traditional firm to do a traditional randomized, stratified sample of telephone interviews. I was dubious about this approach in reaching non-English speaking poor.

I used a separate and very non-random approach. Poor-people's activist organizations were contacted to recruit their members for face-to-face interviews using the same questionnaires.

To the astonishment of all, the results for the low-income people on the traditional survey were so close in outcome to the solicited poor people as to be virtually identical on all the survey findings. Survey researchers responded that the data was very robust, meaning that the results are clearly established in the population being sampled and that these results will stand out regardless of methodology.

We Must Be Very Alike

On many subjects, focus groups of non-randomly selected people in very small numbers have the same results as large, careful surveys. But why not? Most people hearing the same story about a murder will react the same way, otherwise there couldn't be large audiences for films and TV shows. What all of this means is that the whole is less than the sum of its parts.

Before and After Enlightenment

Roberto Mangabeira Unger, a law professor turned social thinker at Harvard, argues that the Enlightenment is about the proposition that the total is equal to the sum of its parts. (See his Knowledge and Politics, Free Press, 1976.) The prevailing world views before the Enlightenment included God, morality, destiny, and spirituality. All of these are based on the concept that the total is more than the sum of its parts. We are of course speaking metaphorically here about teleological paradigms.

But it appears to me that the world is simpler than it looks. When you've seen a few trees, you've seen many; when you get older, there seem to be fewer different kinds of faces in the world, and when you want to get something done, it takes fewer phone calls to get better results. Learning more about the world&emdash;really the world of our people and our culture&emdash;means that living becomes easier as we mature. This is a consequence of the total being made up of many non-independent parts. We grow to understand people and sense the interconnections that make behavior around us more accessible to our desires.

If this analysis is even slightly valid, we should find that pure science is wresting fewer striking insights from the tangible world over the coming decades, while the social sciences will rain abundant excitement upon us. That would be great news.

Michael Phillips, 1986 (revised 2000)


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