I have two variables (group, achievement level). I want to check the effect of an intervention on different achievement levels. For example, I want to check whether there is an increase in achievement scores in low achievers, average and high achievers. Please suggest me which statistical tool should I use? Shall I use individual t-test as I have found in many articles? Or I should use mixed ANOVA?
You say achievement level is an independent variable, then talk about it as a dependent variable. Do you have two scores per person (e.g. a pre-treatment score and post-treatment score) and you are interested in the difference between those scores? If so, it sounds like what you want is simple factorial ANOVA. Predict post-treatment achievement levels based on group, pre-treatment achievement levels, and their interaction. The interaction will tell you if the effect of treatment depends on the level of pre-treatment achievement level.