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I'm new to statistic tests so I need a little bit of help with them. Most of my data has distribution similar to the histogram below.

enter image description here

As it can be seen from the histogram, the data is positively skewed (for example, calculated skewness for this particular variable lol$Total_per_100_k is 1.286938). Most of my sample sizes are somewhere between 80 and 170. I do not know the distribution of any of my variables. Which tests can I use on this data?

For example, which tests can I use to test if the mean of the sample is greater than some value? I'm not sure if I can use one sample t-test because my data doesn't have normal distribution. But my samples are bigger than n=50, so maybe I can use t-test?

When I log-transform the data, the transformed data has normal distribution. But how well can those results (results from tests done on transformed data) be applied to the original data?

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  • $\begingroup$ 0. Welcome to CV.SE. 1. Off the bat, if you are worried about normality you might want to consider a non-parametric test (e.g. as Wilcoxon-Mann-Whitney). 2. We have some excellent threads on this already, (e.g. Should I use t-test on highly skewed and discrete data?, Should I use t-test on highly skewed data ? Scientific proof, please?) so I would suggest viewing them. 3. The skew does not seem horribly pathological so I suspect that the sample mean converges in distribution to a Gaussian. $\endgroup$
    – usεr11852
    Jun 5, 2021 at 13:14
  • $\begingroup$ That histogram might look like a gamma distribution ... if you want more help than a few links, you need to tell us your research hypothesis and other context ... $\endgroup$ Jun 6, 2021 at 20:41

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