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I would like to test whether my data reasonably satisfies the normality assumption necessary to apply a t-test.

My understanding is that, to apply a t-test, the distribution itself does not need to be normally distributed as long as the mean of samples of size n drawn from the distribution is normally distributed.

I have a sample of 200 points and I would like to test that assumption. Would it make sense to draw several samples with replacement of size, say, 30 from my larger dataset to generate a histogram?

Or would the resulting histogram be hopelessly biased towards my larger dataset? How much valid would this histogram be? Worthy of mention in a publication? Informally worthy to go ahead and run the t-test?

Thanks

marcotama
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    "My understanding is that, to apply a t-test, the distribution itself does not need to be normally distributed as long as the mean of samples of size n drawn from the distribution is normally distributed." --- (1) the means of random samples of size n will not actually be normally distributed unless the original distribution was normal. However, such means may be approximately normal (but n=30 doesn't guarantee this). 2. A t-statistic has a numerator and a denominator; you can't just consider the numerator. – Glen_b Mar 07 '19 at 05:29
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    The short answer is no, but drawing samples *the same size* as your original sample will work, as illustrated by my post at https://stats.stackexchange.com/a/69967/919. This is a (parametric) *bootstrap distribution* of your statistic (to wit, the mean). A non-parametric approach (plain vanilla bootstrapping) ought to work fine. – whuber Mar 07 '19 at 16:33

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