Higher values of the t-score indicate that a large difference exists between the two sample sets. But is it ok, to get t-score more than 15 on df (599).
It's not quite true that "higher values of the t-score indicate that a large difference exists between the two sample sets". "Large difference" would need to be defined in terms of the difference in means, pooled variance, and sample size.
But, anyway, yes, it's quite possible to get a t-value greater than 15 with that sample size. For example, if you compare the one group with integers from 1 to 300 and another group with integers from 150 to 450, the t-value will be 21.
You may want to combine all groups into a single model, which would be a two-way anova. It depends on you purpose and the meaning of the data and groups.
I have three IV in study (PhD work) as seperate objectives (1,2,3), among them two IV are Dichomatic by nature and only one IV is Polytomic. For the Dichomatic objectives, I am applying t-test and for polytomic using Anova. But, in one of the Dichomatic objective; t- value is higher in each group. I am seeking constructive suggestions so that I can defend it.
It is no surprise that you get t-score more than 15 on df (599). However, this high t-score and corresponding low p-value may not indicate a real or practical significant difference between the two samples.