Statistical test: newbie needs help on data analysis


I'm a newbie on data analysis and would like to have some advice on how to precede to analysis the following project. The study in concern is a research design with one control and one experimental group. The experimental group attends a specific training program over three week’s time while the control group receives no special training. Assessment on achievement of both groups on several tasks had been made at the beginning, the end of the first week and finally at the end of the third week. The idea is to test whether the training program has any impact on the performance of the subjects.

The subjects are recruited by peer referral, i.e. non-random sampling but they are randomly assigned to the control and experimental group.

My question is: Can I still use the method of ANOVA if the sample is recruited by random sampling? Are there any other statistical tests that I can use in analysis the result? I would be much grateful if anyone can give me a hand on this.

here is what would do
1. Get 2 groups
2. Get their test data for first and third week
3. Run ANOVA single factor ( well, I don't know if you have more independent variables). Your Ho would be there is no difference in mean scores between the groups ( i.e. training sucks:p:p).
4. Set rejection rule. Compare your Fcrit and F calc.
5. get conclusion