![]() ![]() Galton had grouped his results by intervals of 1 inch, and in consequence, if a given child's recorded height were plotted against its recorded mid-parent height, many points would be superimposed on top of each other. For the male children they were unadjusted.įigure 1 is a modern graphical representation of Galton's data. Of course, as previously noted, for the female children the heights were also multiplied by 1.08. (The mean number of children per couple was thus just over 4.5 – families were larger in those days.) He represented the height of parents using a single statistic, the “mid-parent”, this being the mean of the height of the father and of his wife's height multiplied by 1.08. Galton's data consisted of 928 adult children and 205 “parentages” – that is to say, father-and-mother couples. The year being 1886 the computer in question was, of course, a human and not an electronic assistant! The more interesting point, however, is that Galton is describing what we would now call robustness in statistics – and, simultaneously, provides an early example of what is now recognised as a general scientific phenomenon: scientists never seem to fail the robustness checks they report. To use decile to mean tenth – as when, for example, speaking of students “in the top decile” (according to their examination marks) – is not only pompous but also wrong and means that yet another word will eventually have to be invented to perform the function that Galton created decile to fulfil. There are, pretty obviously, ten tenths of a distribution, but there are, slightly less obviously, only nine deciles, since the deciles are the boundaries between the tenths. Of course, words have a way of developing a life of their own, so that, unfortunately decile is increasingly being applied to mean tenth. For example, correlation and deviate are due to him, as is regression, and he was the originator of terms and concepts such as quartile, decile and percentile, and of the use of median as the midpoint of a distribution 2. Many words in our statistical lexicon were coined by Galton. Galton was a brilliant natural statistician. In fact he subsequently freely acknowledged his weakness in formal mathematics, but this weakness was compensated by an exceptional ability to understand the meaning of data. He dabbled in medicine and then read mathematics at Cambridge, but eventually had to take a pass degree. Galton's later progress in education was not quite so smooth. And before you get too impressed, his birthday was February 16th so he was very nearly five! Apparently Galton was also a truthful child, since, having written the letter, he had realised that what he had claimed about the numbers 9 and 11 was not quite true and had tried to obliterate them.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |