- Physically mismeasured skulls so that their cranial volumes would match his expectations about racial differences in cranial volume
- Statistically manipulated population means by taking averages of individual skulls rather than averages of population averages, hence biasing his "Indian" means to be lower
Furthermore, they show that Morton's supposed statistical manipulation had very little effect: the difference was only 0.3 cubic inches. Not only this, but Gould fudged his own measurements which were supposed to proved that different populations did not differ in cranial capacity:
Gould's reanalysis of Morton's 1849 shot-based data resulted in a Native American mean capacity of 86 in3 rather than Morton's original 79 in3. Gould obtained his new average by again taking the group mean of Native American populations with four or more crania. But Gould also applied an additional restriction: he only included Native American crania that Morton had also previously measured with seed. This restriction is entirely arbitrary on Gould's part, as Morton's publications and analyses for his seed- and shot-based measurements are completely separate (1839 versus 1849), and Gould did not apply this restriction to the other groups he reanalyzed in Morton's shot-based data. If this restriction is lifted, Gould's Native American average would be reduced to about 83 in3, considerably below his reported 86 in3.
In other words, Gould's bias is about an order of magnitude higher than Morton's presumed "bias".
It is remarkable that 30 years after the Mismeasurement of Man Gould's errors are uncovered. Why did it take so long? While one could understand why the (totally unfounded but -on the surface- plausible) idea of measurement bias could have gone unnoticed until someone actually re-measured the skulls, but the statistical error that Gould committed was there for anyone to see.
From the paper:
Of the substantive criticisms Gould  made of Morton's work, only two are supported here. First, Morton indeed believed in the concept of race and assigned a plethora of different attributes to various groups, often in highly racist fashion. This, however, is readily apparent to anyone reading the opening pages of Morton's Crania Americana. Second, the summary table of Morton's final 1849 catalog  has multiple errors (Dataset S3). However, had Morton not made those errors his results would have more closely matched his presumed a priori bias (and see Box 4). Ironically, Gould's own analysis of Morton is likely the stronger example of a bias influencing results .First, there is a conflation here between "believing in the concept of race" (which is in no-way invalid, and certainly its validity or lack thereof is not the subject of this paper) and "assigning a plethora of different attributes..." which may indeed be true, but completely irrelevant to the actual quantitative measurements of skulls.
What is most interesting is that Gould's analysis of Morton's work shows clear evidence of bias in favor of his own hypothesis ("Morton was a racist, different races have not much different cranial capacities"), rather than the opposite. Nonetheless, Gould has been viewed by some as some sort of progressive enlightened intellectual, whereas Morton is vilified as a bad scientist who fudged his data because of his racist bias.
Morton may have been a racist, but his data were not provably the product of his racism. Gould was a non-racist, but his data was clearly the product of his biological egalitarianism and/or his quantitative incompetence.
PLoS Biol 9(6): e1001071. doi:10.1371/journal.pbio.1001071
The Mismeasure of Science: Stephen Jay Gould versus Samuel George Morton on Skulls and Bias
Jason E. Lewis et al.
Stephen Jay Gould, the prominent evolutionary biologist and science historian, argued that “unconscious manipulation of data may be a scientific norm” because “scientists are human beings rooted in cultural contexts, not automatons directed toward external truth” , a view now popular in social studies of science –. In support of his argument Gould presented the case of Samuel George Morton, a 19th-century physician and physical anthropologist famous for his measurements of human skulls. Morton was considered the objectivist of his era, but Gould reanalyzed Morton's data and in his prize-winning book The Mismeasure of Man  argued that Morton skewed his data to fit his preconceptions about human variation. Morton is now viewed as a canonical example of scientific misconduct. But did Morton really fudge his data? Are studies of human variation inevitably biased, as per Gould, or are objective accounts attainable, as Morton attempted? We investigated these questions by remeasuring Morton's skulls and reexamining both Morton's and Gould's analyses. Our results resolve this historical controversy, demonstrating that Morton did not manipulate data to support his preconceptions, contra Gould. In fact, the Morton case provides an example of how the scientific method can shield results from cultural biases.