Up on checking my data (large sample size of 11,008) on histogram, it showed almost normally distributed, slightly skewed to the one side. But the Kolmogorov-Smirnov Test for Normality indicated that my data is not normally distributed. I have transformed my data but still end up with a non-distributed data.

My plan was to use an independent Sample t -test to compare the mean difference in two groups. But the independent Sample t -Test needs a normally distributed data as an assumption.

My question goes like, since the histogram almost indicate a normal curve and I am using a large data set shall I drop the assumption of normality and use the independent Sample t -Test or shall I opt for non-parametric tests?

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