Here is a clip from the SCOTUS blog's analysis [Note: In the federal system, 3-judge panels hear all appellate cases, and one judge writes the opinion for the panel.]:
Other than Ricci, Judge Sotomayor has decided 96 race-related cases while on the court of appeals.In one case, Sotomayor "dissented from the majority’s holding that the NYPD could fire a white employee for distributing racist materials."
Of the 96 cases, Judge Sotomayor and the panel rejected the claim of discrimination roughly 78 times and agreed with the claim of discrimination 10 times; the remaining 8 involved other kinds of claims or dispositions. Of the 10 cases favoring claims of discrimination, 9 were unanimous. (Many, by the way, were procedural victories rather than judgments that discrimination had occurred.) Of those 9, in 7, the unanimous panel included at least one Republican-appointed judge. In the one divided panel opinion, the dissent’s point dealt only with the technical question of whether the criminal defendant in that case had forfeited his challenge to the jury selection in his case. So Judge Sotomayor rejected discrimination-related claims by a margin of roughly 8 to 1.
Of the roughly 75 panel opinions rejecting claims of discrimination, Judge Sotomayor dissented 2 times.
Given these statistics, the SCOTUS blog concludes that: "[I]t seems absurd to say that Judge Sotomayor allows race to infect her decisionmaking." I concur. Alas, I am afraid that conservative opposition to Sotomayor has absolutely nothing to do with "facts." Accordingly, these types of studies may have very little impact, if at all, on the negative rhetoric.