I think under current budgets, any student achievement could be linked to parent involvement.
That opinion aside, yes, my school can link their parent group activities to student achievement. At least I know the kindergarten can.
There are two 28 student kindergartens run by one teacher and an assistant teacher in our school. Because of parent involvement, those kids get individual treatment that I never would have thought possible.
We have an excellent teacher who uses the helpers to take students aside in small groups. As well as normal lessons, she manages to do about 8 daily reports on students working on certain problems - ie talking in class, staying focussed, ect.
It's a combination of a wonderful teacher and a set of volunteers that make it a success despite the large class size.
In other grades, we help students drill individually for spelling bees and do other curricular enhancing activities.
Also, we have 400 students in the school and at last count 90, including kindergarteners, were signed up for the science fair. Some, of course, signed up for extra credit in a class. But still....
We just had a meeting last week discussing our goal to become a "Blue Ribbon" school. We will be working on a plan with teachers and the principle on how to get there.
If that's not proof that parent groups are helping in the actual education process, I want to know what is....and we'll find a way to emplement it.