Maurice Kendall - Work in Statistics

Work in Statistics

In 1938 and 1939 he began work, along with Bernard Babington-Smith, on the question of random number generation, developing both one of the first early mechanical devices to produce random digits, and formulated a series of tests for statistical randomness in a given set of digits which, with some small modifications, became fairly widely used. He produced one of the second large collections of random digits (100,000 in total, over twice as many as those published by L. H. C. Tippett in 1927), which was a commonly used tract until the publication of RAND Corporation's A Million Random Digits with 100,000 Normal Deviates in 1955 (which was developed with a roulette wheel-like machine very similar to Kendall's and verified as "random" using his statistical tests).

Kendall and Babington-Smith used four separate tests to determine whether a given sequence of digits was "random" (or "unordered"). The first was a frequency test, which looked to make sure that the count of each digit in a sequence was close enough to expected probabilities ("close enough" was determined by the use of a chi square calculation). If one were rolling an ideal six-sided die, over the long run one would expect to get an equal number of ones, twos, threes, etc. The second test was a serial test, which looked at the expected and observed frequencies of pairs of two digits (01, 11, 12, etc.), which got around the problem of sequences such as "1234512345" which would pass the frequency test but be decidedly non-random. The third test was another type of frequency test, this time for the expected and found set of five-digit sequences, known as a poker test, after the card game. The fourth test was known as the gap test, which looked for expected gaps between individual digits (usually between zeros) in long sequences, comparing observed counts ("01230" would be a gap of three digits between the zeros, "0120" would be two, etc.) with their statistical probabilities. If a set of numbers passed all four tests, it was considered by Kendall and Babington Smith to be "random enough" for most usage. They also developed the notion of "local randomness", noting that in any sufficiently long sequence of truly random digits there would be sets which would look exceedingly unrandom (such as a string of many zeros together). They concluded that these small cases of local un-randomness in an overall random sequence should not be discarded, but that care must be taken in the uses of random number sequences to make sure such "patches" of data did not overly add bias to the results.

In 1937, he aided the aging statistician G. Udny Yule in the revision of his standard statistical textbook, Introduction to the Theory of Statistics, commonly known for many years as "Yule and Kendall". The two had met by chance in 1935, and were on close terms until Yule's death in 1951 (Yule was godfather to Kendall's second son).

During this period he also began work on the rank correlation coefficient which currently bears his name (Kendall's tau), which eventually led to a monograph on Rank Correlation in 1948.

In the late 1930s, he was additionally part of a group of five other statisticians who endeavored to produce a reference work summarizing recent developments in statistical theory, but it was cancelled on account of onset of World War II.