What can we do?

In this triad, confusion reigns.


There are two aspects that leave us in confusion at best, delusion at worst.

• Intellectual: In the worlds of K12, or even K16, we are much too rarely taught about the world of chance, that nature is indeed probabilistic in its most fundamental and governing manifestations. The short answer is we are too often intellectually unaware of the many systems of probability, their expressions, and how their expressions affect our daily lives.
• Emotional: Most of us have a need to understand our purpose in life and what happens after life that are met with dogma dating back millennia. For the ordinary human being, they work quite well enough. But no dogma, whether classical philosophy or religion can explain how nature actually works. So we project our particular dogma upon others who in turn project their own versions back upon us. What else can we do? Unless these projections fit, there can be little mutual understanding, much less dialogue. Nature is so complex that only disciplined observations and experiment can elucidate its secrets. Dogmas did not come about that way--though they were the best available explanation of their times. Only with the rise of science did the dogmas of history begin to fail their basic purpose. Dogmatic projections fail to provide understanding sufficient to provide the substance necessary to improve our lot and extend our lives to their natural limits.

What follows deals with the intellectual issue, for it alone has the property of consilience, where all knowledge must be coherent throughout all branches of science and its descriptor, mathematics. Unfortunately it is too little understood, even among scientists.

Science hasn't failed, but some of its erstwhile practitioners have--big time. Why? The answer is simple. But it is not simple in practice.

I had the personal good fortune to learn about statistics in a laboratory where our mission was to invent and develop new alloys for aerospace applications. Upon returning to graduate school to fill out my education, I discovered there not a single course on statistics in the curriculum. I asked the dean, why? His reply: "That's a matter for the math department." I was stunned into speechlessness. In fact, along with the laws of physics, statistics is common to all branches of science. If you know statistics, all you need to perform research in any field is the vocabulary of that field. How a first tier graduate school can fail on that point still escapes me. Well, one tentative answer is obvious: Our inherent tendencies toward authoritarianism have led department heads collectively into departmental dogma.

I encountered the fall out from this very early in my career. I worked with a wonderful man who was charged with solving a particular technical problem in regression. He used the formulae correctly in arriving at a result he just could not fathom. The slope was not steep; the effect he found after much experimenting was less strong than he believed it should be. In a group meeting, he asked all of his colleagues why his hoped for result was not appearing. He gave several reasons why the slope should be steep, about 30 degrees instead of the 15 degrees he found. He went on to explain that regression toward the mean under-estimates the true slope. That happens to be so even though the regressed slope still provides the most predictive estimate of the value of the dependent variable, Y, on an X-Y plot. On this particular point he was our teacher.

For example, in a notable historical example, Sir Francis Galton plotted the height of fathers against the height of their sons and discovered sons of tall fathers tended to be tall, but on average not as tall as their fathers. He also showed that sons of short fathers tended to be short but taller than their fathers--according to regression. He concluded that eventually all men would be of average height, This cannot be of course; height is a variable that can be described as by a normal distribution, the familiar bell curve. Understanding why Galton erred is simple. Take two normally distributed variables having the same variance and regress them in opposite ways, each variable being both independent and and dependent in turn. The slopes are not inverses of one another, even though each minimizes the variance--the average sum of the squares of all deviations of the dependent variable from the mean.

As common as this "error" is, that was not my friend's main problem. As the discussion continued, we eventually realized we were misunderstanding the difference between significance and strength of effect. The first deals only with the likelihood that there is no effect. The latter only estimates how strong the effect is.

Not just my friend, but the rest of us too, were deluded by the semantics. Does significance mean extraordinarily right? Of course. But in its statistical context, significance says nothing at all about the strength of effect. But most of us learned early in life significance also means magnitude. A significant grade is a slope difficult to run up. It is steep. Strength of effect is critical: to our health, welfare, economy, indeed to humanity itself. But as used in science, the word significance expresses only the likelihood that the result is wrong altogether--that there is no slope whatsoever.

This was the rub in our case. English words often have multiple meanings, so the context matters. But unless we have some expertise in the field of statistics we are very unlikely to realize that the word "significance" used by statisticians has a more restricted meaning than we learned early on. My friend had mistaken a significance of 0.01 (higher than 0.05, the conventional level) as implying the strength of effect should also be high. In fact, significance, as used by statisticians, is set by the investigator. For a survey looking for possible correlations, 0.05 is a quite reasonable value. For a commercial airliner, relying on perhaps thousands of critical correlations, one would only be comfortable with significance levels of 0.0000001 (or 0.00001%) that there is no correlation. The sheer magnitude of potential errors in design or analysis is just one reason why the failure rates are so high in space exploration, relative to air travel.

In the real world, a very weak effect can by highly significant; conversely, a very strong effect can be insignificant, even unreal.

Since the arena of greatest abuse is in the medical and social sciences, it behooves all of us to at least understand the meaning of the word significance as drug companies and governments use, or misuse. it. We will be the better for it.

The great irony is that humanity as a whole seems to prefer myths to facts.

It is just too easy for us, statistics, be damned, to join others like ourselves in following the charismatic, be s/he wise or unwise, intelligent or not, moral or immoral, well balanced or sociopathic. Violence, of course, is the byword for the sociopath whereas it is the option-of-last-resort for the rest of us. Emotional and economic fall out are virtually certain to follow. Mythos takes over, we believe, but too many of us fail to think--is our leader in touch with reality? We have no answer unless we ourselves have a reasonably accurate perception of human affairs from the individual, family, society to inter-society levels.

Edward O Wilson is the pioneer in evolutionary biology, where one finds the origins of such behaviors, both of the leaders and the led. About half of our inborn traits we share with ants who belong to a different taxonomic phylum! This is not a statistical fluke, it is a demonstrable fact, with a significance so high that the likelihood of that being a chance event is much too close to zero to matter. This is especially so since animals closer to us taxonomically exhibit behaviors ever more closely to our own. Knowing just that simple fact, and why it is so compelling statistically, should arm us to be skeptical of the motives of those who preach bigotry, racism, and sexism. Such behaviors led to survival in the jungle, but they are detrimental to civilization.

Visit Scientific discipline our take, and "Odds Are It's Wrong" by sciencenews.org for more.