Randomness by Deborah J. Bennett

Author:Deborah J. Bennett
Language: eng
Format: mobi, pdf
Published: 2009-09-06T16:45:00+00:00

Weldon used these artificial data as a teaching tool, since it was so easy for an audience to see how a pattern could arise from even random data like dice throws. Figure 19 displays Weldon's experimental results. The columns are labeled 0 through 12, indicating outcomes possible on the first throw, and the rows are labeled 12 through 0, the outcomes possible on the second throw. The numbers in the cells of the table represent the total counts of particular outcomes on the first and second throws. We can clearly see the strong pattern in this data. When the number of dice showing four or more spots on the first throw is small, the number of dice showing four or more spots on the second throw tends to be small; when the number of dice showing four or more spots on the first throw is large, the number of dice showing four or more spots on the second throw tends to be large. This correlation accounts for the pattern we see in the table: the largest counts of trials appear to cluster from the lower left corner of the table to the upper right corner.

In 1907 A. D. Darbishire performed an interesting series of experiments in an "attempt to make the phenomenon of correlation clear to an audience previously unfamiliar with it."" Darbishire expanded on Weldon's experiment in order to illustrate thirteen levels of correlation. Just as Weldon had done, Darbishire rolled twelve dice and recorded the number of dice showing four or more spots. Some of the dice were rerolled and, along with those left on the table, constituted the second throw, where once again the number of dice showing four or more spots was recorded. As in Weldon's experiment, the rolls were correlated, since the dice left on the table constituted part of both throws.

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