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An Early Statistical Calculation

In the winter months during the 1950s and 1960s some of the statisticians in Ottawa used to meet informally from time to time to hear one of their number read a short paper on the work he or she was doing. The meetings were presided over by Dr. John W. Hopkins, a very genial and erudite man, who was in charge of a small biometrics unit in the Division of Applied Biology of the National Research Council of Canada. The speaker acted as the host that month and provided tea and cookies. As I was one of the few members of the group who had had any experience with computers and also had access to one of the few computers in the Ottawa area, I was asked to address the group and give a demonstration of the use of computers in statistics. This talk took place on October 25, 1956.

The problem I chose for the demonstration was the calculation for a Latin square of arbitrary size for which the total sum of squares was partitioned into those portions for rows, columns, letters and residuals. In the absence of floating-point arithmetic routines all of the arithmetic had to be done in fixed-point so that an integer scale factor had to be carried throughout the calculations and constantly updated in order to keep track of the decimal point. The data used for the demonstration were for a three-by-three Latin square. The output from the original demonstration is no longer available, but the calculation fortunately was repeated a few months later and the output is shown in the accompanying figure. The single number shown in the first row gives the scale factor. The remaining rows of the output give the components of variation for rows, columns, letters, residual and total while the columns give the sums of squares, degrees of freedom, mean squares and F-ratios. For example, the numbers in the second row when properly scaled are 3134.8, 2, 1567.4 and 1.361181. Lack of proper identification of the output and the absence of decimal points may be attributed to having to fit the entire program including what amounted to the simulation of floating-point arithmetic into 1024 words of storage.

I can remember the day of the talk very well because afterwards I went downtown with my friend Jim Howland, who has been mentioned earlier in connection with the Meccano Differential Analyzer at the University of Toronto, to pick up my new car, a Volkswagon Beetle. It cost, with a few extras, $1651, and I sold it seven years later for $300 when we left Ottawa for the University of Alberta. It was the only car I have ever owned.


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