So, for an experiment I analyzed behavioral data of two different treatment groups with $n = 30$ for each of two groups, so 60 subjects in total. I used a computational model to analyze the data and calculate a specific score that describes the motivation to obtain a specific reward.
This score is a continuous variable, but according to a Shapiro-Wilk test, the distribution of the data is non-normal. According to a two-sided Wilcoxon rank sum test, the difference between both groups is not significant ($p \approx .08$). However, after performing an alternative (model-free) analysis by using logistic regression, I actually found a significant effect of treatment group on behavior.
Additionally, after performing a two sided t-test with the computational data, I also found a significant difference between both groups ($p \approx .04$).
Now the information that I have are quite contradictory. Some say that a sample size of 30 is sufficient to use a t-test, even if the data is not normally distributed. Other sources say that I still should use a u-test, even for "larger" sample sizes.
So I'm a bit confused. Of course, the results of the t-test fit with my hypothesis and the model-free findings. On the other hand, I want to use the "appropriate" test, not the one that confirms my hypothesis.
What do you think? Is my sample size big enough to use a t-test? Or should I go with the u-test, even though it contradicts the results of my alternative method?