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| Galton   | R Documentation   |
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Galton's data on the heights of parents and their children
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Description
~~~~~~~~~~~

Galton (1886) presented these data in a table, showing a
cross-tabulation of 928 adult children born to 205 fathers and mothers,
by their height and their mid-parent's height. He visually smoothed the
bivariate frequency distribution and showed that the contours formed
concentric and similar ellipses, thus setting the stage for correlation,
regression and the bivariate normal distribution.

Usage
~~~~~

::

    data(Galton)

Format
~~~~~~

A data frame with 928 observations on the following 2 variables.

``parent``
    a numeric vector: height of the mid-parent (average of father and
    mother)

``child``
    a numeric vector: height of the child

Details
~~~~~~~

The data are recorded in class intervals of width 1.0 in. He used
non-integer values for the center of each class interval because of the
strong bias toward integral inches.

All of the heights of female children were multiplied by 1.08 before
tablulation to compensate for sex differences. See Hanley (2004) for a
reanalysis of Galton's raw data questioning whether this was
appropriate.

Source
~~~~~~

Galton, F. (1886). Regression Towards Mediocrity in Hereditary Stature
*Journal of the Anthropological Institute*, 15, 246-263

References
~~~~~~~~~~

Friendly, M. & Denis, D. (2005). The early origins and development of
the scatterplot. *Journal of the History of the Behavioral Sciences*,
41, 103-130.

Galton, F. (1869). *Hereditary Genius: An Inquiry into its Laws and
Consequences*. London: Macmillan.

Hanley, J. A. (2004). "Transmuting" Women into Men: Galton's Family Data
on Human Stature. *The American Statistician*, 58, 237-243. See:
`http://www.medicine.mcgill.ca/epidemiology/hanley/galton/ <http://www.medicine.mcgill.ca/epidemiology/hanley/galton/>`_
for source materials.

Stigler, S. M. (1986). *The History of Statistics: The Measurement of
Uncertainty before 1900*. Cambridge, MA: Harvard University Press, Table
8.1

Wachsmuth, A. W., Wilkinson L., Dallal G. E. (2003). Galton's bend: A
previously undiscovered nonlinearity in Galton's family stature
regression data. *The American Statistician*, 57, 190-192.
`http://www.cs.uic.edu/~wilkinson/Publications/galton.pdf <http://www.cs.uic.edu/~wilkinson/Publications/galton.pdf>`_

See Also
~~~~~~~~

``PearsonLee``, ``galton``

Examples
~~~~~~~~

::


    data(Galton)

    ###########################################################################
    # sunflower plot with regression line and data ellipses and lowess smooth
    ###########################################################################

    with(Galton, 
        {
        sunflowerplot(parent,child, xlim=c(62,74), ylim=c(62,74))
        reg <- lm(child ~ parent)
        abline(reg)
        lines(lowess(parent, child), col="blue", lwd=2)
        if(require(car)) {
        dataEllipse(parent,child, xlim=c(62,74), ylim=c(62,74), plot.points=FALSE)
            }
      })

