A researcher wants to test whether two services that purport to increase GRE scores differ in their effectiveness. One is Princeton Review (PR), the other is Kaplan (KAP), a variable referred to as...

A researcher wants to test whether two services that purport to increase GRE scores differ in their effectiveness.  One is Princeton Review (PR), the other is Kaplan (KAP), a variable referred to as GRE-testype.  She also decides to look at both the verbal (V-GRE) and quantitative (Q-GRE) scores after the training, a variable labeled as Service.  She randomly assigns 40 students to each of the programs (total N = 80).  The scores below reflect the mean score increases for the students:

SS_GRE-testtype
= 3.76       SS_Service
= 3.03        SS
_{GRE-testype X Service}
= 37.41     SS_WITHIN
= 652

Use alpha .05 for all tests and explain the results in terms that could be understood by a lay audience.