How to determine if my sample size is large enough I currently have 146 participants in 4 groups as follows:  


*

*group 1 = 46

*group 2 = 40

*group 3 = 29

*group 4 = 37


Each group completes the same 20 trials, but the groups have different characteristics (which is why they are separated).
I'd like to know if I have enough participants per category to get statistically significant results or if I need to keep running the study and get more participants. 
 A: I am guessing you are planning to perform an anova.
Determining whether you have a large enough sample size depends not only on the number within each group, but also on their expected means, standard deviations, and the power you choose.
So far you have given us:
$n_1=46, n_2=40, n_3=29, n_4=37$,
but previous studies/analyses should inform your expectations about the group means and standard deviations.
Finally, .80 is commonly used as a threshold for power. While your alpha (e.g. $.05$) can be thought of as Power is the threshold for true positives.
There are many tools (readily available through a Google search) that can help you with power and sample size calculation. Good luck.
A: it depends on the standard deviation that you're observing.
say you ask group 1 and group 2 a yes/no question:
if 100% of group one answered "yes" and 100% of group two answered "no" then you aren't going to need more than fifteen respondents in each group to conclude that group one is statistically significantly different from group two.
if, however, 45% of group one answered "yes" and 50% of group two answered "yes" then you are going to need much more sample to detect a statistically significant difference.
to get an idea of what sample size you need to detect a statistically significant result, perhaps try punching some numbers in the "average, two sample" power calculator here:
https://www.dssresearch.com/KnowledgeCenter/toolkitcalculators/statisticalpowercalculators.aspx
