I am having difficulty in exactly understanding several statistical tests, such as the t-test and ANOVA test. These tests require that the data we use be normally distributed.
However, whilst sharing my experience in analyzing data a bit, I have analyzed several data sets from numerous sources online (web scraping, open-accessed data sources online, etc.), with the considerably high number of samples (hundreds, thousands). An example of the data in question is the amount of donation given to certain campaigns in a fixed periods of time (day 1 at 1pm, day 2 at 1pm, etc.).
And when I tested whether the distribution of the data was normal, using visual aids (histograms, Q-Q plots) and Shapiro-Wilks test, they all showed me that the data is not normal. For example, Shapiro-Wilk test gave a p-value of so small (less than 0.00000000000000022), of course, the null hypothesis has to be rejected, i.e. the data is not normally distributed.
Because I read in articles like in this link, it says
However, even if the distribution of the individual observations is not normal, the distribution of the sample means will be normally distributed if your sample size is about 30 or larger
So naturally, I am confused, is my data normally distributed or not? How often do you encounter normal and not-normal distribution, in real-life data?
EDIT Following the response by @hssay in his answer and comments, my main objective here is that I want to do ANOVA test to determine the relationship between my numerical and categorical data. But ANOVA needs the data to be normally distributed. So now I am confused as to how to conduct it since I have a "sample" consisting of thousands of rows of data that I took only once.