information provided in Tables I to IV so as to calculate the IQ distribution in narrower categories, reproduced as Table 4.5.
Rubin demonstrated (a) that there were suspiciously small counts in the 90-1 category, much smaller than would have been predicted if the data conformed to a normal distribution (8 observed and 21 expected), and that (b) the distributions of fathers and sons were more similar to one another than either is to the normal distribution, and only one of the entries (children in the range 110-15) corresponded with the numbers predicted by a normal distribution. In particular, Rubin noted a bizarre feature of the fathers' and sons' IQ scores. If we ignore the 90-1 band, there is nearly always a difference between the numbers of fathers and of sons within each individual band. But when one combines neighbouring bands, e.g. IQs 50-60 with IQs 60-70, and IQs 70-80 with IQs 80-90, the number of fathers and sons becomes identical. In other words, the discrepancies in individual bands are virtually always precisely compensated for by an opposite discrepancy in the next band. It is difficult to see how this could have happened by chance. Rubin concluded:
if the IQ data are approximately N (100, 15), the patterns in our Table 1 are suspicious, and if the IQ data are not approximately normal, the excellent fits of the IQ margins in Burt's tables I, II, III, and IV to the N (100, 15) model are suspicious.
He found an additional inconsistency when studying the narrower categories for each occupational group. Table I shows that in class VI there are 20 fathers (11 + 9) with IQs greater than 100, while in Table III Rubin calculated there were 24 with IQ scores more than 103. Rubin said, 'This inconsistency may be the result of trying to create the entries of tables from specified margins, as Dorfman suspects'; but he acknowledged that this inconsistency might be the result of a recording, computational, or typographical error, of which the latter is not unknown in Burt's publications.
Most people, though not all, who have written about Burt's work, and in particular his 1961 paper, agree that Burt provided very poor descriptions of his sources of data and techniques used. For example, Stigler wrote ' Burt's description of his procedure is extremely vague' and refers to 'his unclear explanation of what he did', while Rubin talked of ' Burt's ambiguous labelling of categories'. Dorfman took a stronger line: ' Burt . . . was extremely vague in his descriptions in order to mask his scientific fraud.' Whether or not Dorfman's strong inference is justified, there can be no reasonable doubt, as I have shown above, that Burt's description of his procedures etc. is wholly inadequate.
It is easy to say now that many of the ambiguities and uncertainties surrounding this paper could have been clarified had the editor of the