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This Fall, I was introduced to the "Westat Study" which was
a large study done to evaluate Student Support Services
(TRIO) Programs.  One of their findings was that students
gained 0.10 GPA points (one tenth) for every five hours of
peer tutoring.

Since I had never done a study of GPA rather that course
grade, I used this evaluation method for tutoring.

In my analysis of the 80 students who had all of the
relevant data:
        Students with five or fewer hours of tutoring
actually did worse that students who applied but never used
tutoring by about 0.20 points on semester GPA.
        Students who used five to ten hours of tutoring
increased by 0.50 GPA points on semester GPA from the group
that used less.
        Students that used more than ten hours declined by
0.40 GPA points from the students in the 5-10 hour group.

In my analysis using the average grade (rather than semester
GPA) for each group, I found that:
        Students with five or fewer sessions showed about a
0.20 increase from students who didn't use tutoring.
        Students with five to ten sessions showed a 0.07
increase from students who used less.
        Students in the ten or more session group showed an
increase of 0.22 in the average grade for the course.

These two analyses do suggest a relationship between hours
of tutoring and academic performance in the course for our
students and some improvement in GPA.  The Westat folks
found a way to compare aggregates, which I liked because it
minimizes the "apples and oranges" effect that motivation
may play here a bit.