Ok I finally read this column. What DeSarno is saying is that the Patriots balls and the Colts balls loss of air pressure are different from each other by a statistically significant margin. I haven't run the numbers myself but just by eyeballing them, that looks like a reasonable statement.
However, the main point of AEI's thesis involves the fact that the Patriots' balls were measured right away at halftime, and the Colts' balls were measured 10 minutes later, after they had time to warm up.
All DeSarno does is run an ANOVA (Analysis of Variance) on the numbers. He concludes something which AEI already admitted. On page 2, AEI states:
We find, as the Wells report did, that the evidence suggests on balance that the Patriots balls declined in pressure more than the Colts balls under the maintained assumptions in the report. As we will explain, however, this does not necessarily constitute evidence that the Patriots illegally tampered with their footballs.
All DeSarno is doing is verifying the first sentence of that paragraph.