Monday, November 4, 2013

The Drift Function For Galton's Stature Data

  One can find a drift function for the data in Table I of Galton's Regression towards Mediocrity in Hereditary Stature (1886). The columns designate the average height of the parents, x, and the rows those of the children, x'. The table is reproduced here with nominal heights assigned where they are missing in Galton's table.

One has to use the row heights to compute the expected value of x' and one can find a simple linear fit for the drift function.

The slope is close to -2/3. For the drift function we can define ΔX = x - x0 where x0 is the average height of the children.

There is a stable point at approximately x = 68.7 in. and parents whose average height is above this tend to have shorter children and those below tend to have taller children. Note the similarity of the drift function to the difference between the lines for the parents and the children in Plate IX in Galton's paper.

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