Doing Parametric Tests without normal distribution

[Curtains White]

Hello everyone!
Is it true that when your sample is more than 30 people, you can do parametric tests, even though your sample may not follow the normal distribution?

In my research I have 400 people as a sample, not following normal distribution and someone told me that I can do parametric tests anyway... But I wanted to ask the experts (you) to confirm that in case this is not true.

If someone knows something about that, please(!!!!!!) let me know! Thank you in advance for your time!!

 

[Karabiner]

You need not care for the distribution of your dependent variable anyway, regardless of n > 30 or n <30. Instead, the residuals of your model (e.g. t-test, ANOVA, linear regression) should preferably come from a normal distribution. But it is true that with n > 30 one can assume that the tests are valid, even if the resiudals are not from a normal distribution. You can look for the central limit theorem.

With kind regards

Karabiner