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Suppose I run a t-test and I get the following result:

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The p-value is very small, so I reject the null hypothesis. However, I was wondering if I could say something on the sign of two mean and their relative dimension from this data. Also, can I say something with a significant level of 5% or 0.0001%?

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  1. You can't decide on the significance level of a test after calculating a p-value. If the prespecified alpha level was 0.05, you can say the test is significant at that level. (You don't reject the null hypothesis just because p-value is small, suppose your alpha level was even lower.

  2. You can't say anything about the sign of the two samples that you put in this test. The 95% confidence interval just tells you the mean of X is lower than Y. (the average of the CI will give you the actual mean difference). But X mean could be 100 and Y mean could be 102 or X mean could be -100 and Y mean could be -98 and the results are the same.

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  • $\begingroup$ I see. What about the relative dimension of the two mean samples? $\endgroup$ – qcc101 May 15 '19 at 5:35
  • $\begingroup$ @qcc101 what is "relative dimension"? Do you mean relative direction? $\endgroup$ – AdamO May 15 '19 at 14:24
  • $\begingroup$ Nope, I mean how small or big one is with respect to the other. $\endgroup$ – qcc101 May 15 '19 at 18:31

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