Sorry, Neocon, but you have the idea of regression toward the mean completely screwed up. There is usually regression toward the mean in stationary systems (like sampling with fixed probabilities) but not in growth, trends, or cyclical systems.
Moreover, in coin flipping you do not observe runs of heads being offset by by runs of tails. The key is the concept of Bernoulli trial, in which the probability of each event is independent of all prior events. Thus the probability of any toss of a (fair) coin being a head is independent of the previous tosses. Any decent statistics course will have the students undertake and graph repeated coin tosses. What one finds is in some series, the proportion of heads is greater than 1/2 and sometimes continues to be, although in the limit it converges to 1/2. And the same with tails. It is apparent that you have never performed this experiment in a class.
When events are drawn from a single population, in which the probability of "success" appears to be the same, there is an appearance of regression toward the mean. For example, one takes samples of two tall adults (over 6") and allows them to mate. This results in children who, on the average, are taller than 5'10" (the population mean height) but shorter than 6'. Thus the mean of the children's height regresses toward but not to the mean. But this is not the result of some "shortness factor" making up for a "tallness factor" in the parents. The distribution of children's heights is not independent of the parents' heights. If there was not some dependence (autoregression) the heights of the children would cluster around the population mean instead of being intermediate between the mean height of the parents and the population mean.
Your discussion of weather is an old granny's tale. Actually local climate consists of many different cyclical components along with neighborhood effects. There is no discernible compensation in weather. The rain falls on the just and the unjust alike. |
