I have sixty participants where divided into three stress reduction treatment groups (mental, physical, and medical) and two gender groups (male and female). The stress reduction values are represented on a scale that ranges from 1 to 5.
The question is: "How effective is the treatment program in reducing participant's stress levels?"
Can I use Two-way ANOVA without interaction to calculate how effective is the treatment program?
Yes, the ANOVA is one approach with which you can answer your question. For your design, I would include the interaction, though. If you don't do it, I can't see the added value of having the sample split up by gender. Once you have your ANOVA results and want to answer your question how effective each of the treatments is, that is you want quantify your effect, you have to check the difference estimates for each of the groups. However, I'm not sure whether it is possible to draw an absolute conclusion, at least from what I can see in your design, because you don't seem to have a baseline condition. If so, all you will be able to conclude is that the physical treatment is X more effective than the medical, and so on.
The assumption of normality on which the usual inference would rely won't hold for a 1-5 scale; if you're prepared to treat it as interval and your sample sizes are large, and the effects aren't so large that variance is affected by boundary issues then you may be okay.
Alternatively you can always treat the dependent variable as ordinal and use a model suitable for that, such as a proportional odds cumulative logit model for example.
