Timeline for t-test on highly skewed data
Current License: CC BY-SA 3.0
6 events
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| Nov 18, 2015 at 20:42 | history | edited | zkurtz | CC BY-SA 3.0 |
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| Sep 13, 2013 at 17:13 | history | edited | zkurtz | CC BY-SA 3.0 |
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| Sep 13, 2013 at 16:51 | comment | added | whuber♦ | I have posted an answer to that question. We know (at least approximately) how skewed the data are based on the summary statistics in the question. That skew is so strong that neither 300, nor 3000, nor even 30,000 observations per group will make the sampling distribution of the mean "almost exactly normal." You probably need around 300,000 or so before that claim becomes plausible. Thus we must seek a different explanation for why the two tests agree. Mine is that neither is "well-behaved" rather than that both are well-behaved. | |
| Sep 13, 2013 at 16:36 | comment | added | zkurtz | Great point. I admit, if the data is sufficiently skewed, my argument fails. So the question to me is, exactly how skewed is the data, and is there a formal result out there relating the skewness to the required sample size. | |
| Sep 13, 2013 at 15:34 | comment | added | whuber♦ | When skewness is extreme--as the quoted statistics attest--we have no assurance that the sampling distribution of the mean of 300 or even 3000 samples will be anywhere near Normal. That is why the OP is surprised. You counter that by saying you are not surprised, but that appears to come down to one person's intuition compared to another's. What objective argument can you supply for these data demonstrating that 300 (or 3000) is a large enough sample for the t-test to work well? | |
| Sep 13, 2013 at 1:39 | history | answered | zkurtz | CC BY-SA 3.0 |