Yes Dear, Reliability and Validity also. There are different techniques you can check them on Google.

I will second the previous comments.

You MUST check the psychometric properties of the instrument EVERY TIME you use it. This is because what works for one group might now work for another group. So you have to do a factor analysis to determine of the items you say are reflective of a construct do in fact group together in the minds of your subjects. You have to ensure that there is no cross loading of items across constructs. Cronbach's Alpha and AVE should be assessed, etc.

• I applied factor analysis on statements and derived factors (factor scoresl were taken for further analysis through t-test and ANOVA etc.  As I am not going for CFA is it required to check construct validity (convergent+divergent+nomological) in this case.  What i assume is that, after ensuring content validity and checking reliability through cronbach's alpha on specific derived factors. The only thing, which is required is to cross verify the derived factors through splitting or out sample.  Am I right, please suggest? 

Valid instruments are reliable, you must check construct validity (convergent and discriminant ). 

For details about construct validity, follow my publication "An Easy Approach to Exploratory Factor Analysis",

I have illustrated practical example from marketing literature, it may help.

You can download it free.

http://www.mcser.org/journal/index.php/jesr/article/view/8799

It dependa on the analaysis. U can use Test-retest analaysis, correlational analaysis, or internal consistency tools like cronbach alpha depending on the nature of your study