OK, let's go through the study. They set out three reasons why standards might affect achievement:
1. Achievement will increase because students will study a better curriculum.
2. States won't be able to fiddle with cut scores to make performance appear better than it is.
3. Standardization will reduce redundancy and increase efficiency.
For #1, they looked at the Fordham Foundation ratings of state standards and then compared that to state achievement in 2006 and 2009. They found that quality of standards was not correlated with achievement. However, they did not control for the demographics in the states; they only controlled for CHANGES in demographics in the states between 2003 and 2009. I think that's odd and problematic.
For #2, they found that it wasn't possible to conclude whether increasing cut scores increased proficiency, or increasing proficiency led states to increase cut scores. For what it's worth, #2 doesn't apply to the Common Core standards anyway, since a lot of states have chosen to give their own tests and will continue to be able to fiddle with cut scores.
For #3, they found that within-state variation in test scores is greater than between-state variation in test scores. I really don't think that's relevant to the idea that standardization will reduce redundancy and increase efficiency, though. Of course it will.
Then they go on to make two points:
1. Do not expect much from the Common Core. (By the way, speaking of copy editing, somebody mixed up "infer" and imply" in that paragraph.) Why? Because standards do not necessarily translate into curricula and teaching. I actually agree with this; the Common Core is not a panacea, and anybody who said that it was is a fool.
2. [They don't make a second point, or if they do, I can't find it.]
So, does this study prove that standards have no effect on achievement? I don't think so. I think it's more likely statistical explanation is that standards have an effect on achievement, but it's a small effect, and it's swamped by the long list of factors that have a much bigger effect on achievement.