Tuesday, November 5, 2013

Another Look At The Drift Function For Galton's Stature Data

  The linear fit for Galton's stature data seems to indicate a deviation of the mean height from the stable point and this would be a violation of the regression to the mean. A cubic fit gives better agreement with the law of the regression to the mean. The scales below have been adjusted to show the difference in inches from the stable height.

There are more data points near the origin of the plot and consequently one would expect greater certainty in their position than at the ends. Still the data indicates a weakening of the tendency to regress to the mean. Perhaps this shows more a preference for taller spouses by taller people.

  People are taller now than they were thousands of years ago. This suggests that the stable point has shifted to the right over time and so the drift function must be a function of time. We can allow for this change by replacing the constant coefficients in the drift function by functions of time. Changes in the drift function would result in changes in the observed heights of the population. Some sources of change might be changes in the environment, the selection of stronger, taller men through combat or some bias in the preferences in the population. The drift function may be what's controlling evolution.

  The drift function for the temperature anomaly may be affected by environment factors and consequently be responsible for some change in the mean but with a cubic drift function the tendency to return to the stable point is reduced at points nearby. Random walks would have more of an influence on the observed anomalies making it difficult to tell if there actually is some global warming occurring. This point out a need to be clear about what we mean by global warming. The semantics may be politically correct but are they scientifically correct?

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