I have 12 samples with approx. 50.000 data points each. I got it from a content analysis of Reddit comments. The data is generated by analyzing the comments with LIWC tool and it gives me information for instance about the percentage of pronouns in a comment. The comments represent one year and consists of every publicly availabe comment on Reddit for five particular subreddits.
Central limit theorem says that with a certain amount of samples, the data will be normally distributed. This is also the info I got when asking friends, who are quite good in statistics (Master in econometrics etc), when i asked if i can compare groups with the t-test. But when i plot the data, it looks quite skewed and not normal at all and I wonder when you are not able to accept central limit theorem anymore?
How can I be sure that the attributes of the population is not naturally, non-normal distributed?