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I did a mixed ANOVA with one within subjects factor with two levels 'time' and one between subjects factor (control + intervention). Its a comparison between INT or CON on scores pretraining and posttraining.
The results showed a significant main effect of time from pre to post training but no significant interaction effect. Do I therefore need to run 2 paired t-tests to determine what group had statistical significant difference?
No, your finding indicates that while there is statistically significant change over time (main effect of time), this change does not differ between the groups (nonsignificant interaction between time and condition). Doing paired t-tests for each group, examining the pre-post change, would be misleading and not actually test what you want to know (did the treatment produce more change than would be expected under the control condition).
This is your aim: "... its a comparison between INT or CON on scores pretraining and posttraining." Rephrased you want to know if there is a difference between groups on the test-scores. That is why you use a mixed ANOVA.
If your aim would be: to compare pretraining and posttraining scores (irrespective of the group), you would use a paired t-test.
The results showed a significant main effect of time from pre to post training but no significant interaction effect. Do I therefore need to run 2 paired t-tests to determine what group had statistical significant difference?
A non-significant interaction effect means you can continue to interpret the main effects (the effect of the within-factor 'time' and the effect of the between-factor 'group'). Depending on which program you used, you should see these effects listed in the output.
