Timeline for If we fail to reject the null hypothesis in a large study, isn't it evidence for the null?
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| Apr 25, 2017 at 20:17 | comment | added | Macond | Middle of the confidence interval corresponds to $\mu$'s, which will yield the observed sample mean with higher probabilities. But this is not equavalent to the statement: "$\mu$'s closer to the middle have higher probability of being true mean". As stated many times by others: $P(A|B) \ne P(B|A)$. | |
| Apr 25, 2017 at 17:14 | comment | added | bkoodaa | "this does not mean that there is a higher probability of population mean being close to middle of the interval." -- This can't be correct. I read the paper but could not find anything to corroborate this. | |
| Apr 25, 2017 at 9:31 | comment | added | Macond | Yes this is a misinterpretation. P value is not probability of null hypothesis being true, or strength of evidence in favour of null hypothesis. Similarly, you could make an interval estimate, with sample mean in the middle of the interval, but this does not mean that there is a higher probability of population mean being close to middle of the interval. There is a reference to a good explanation about this misinterpretation in the comment by Dominic Comtois to your question. | |
| Apr 25, 2017 at 8:23 | comment | added | bkoodaa | "Now for what value of μ do we have evidence?" -- We have stronger evidence for values closer to sample mean and weaker evidence for values further from sample mean. How strong or weak depends on sample size and variance. Is there something wrong with this interpretation? | |
| Apr 25, 2017 at 8:02 | history | answered | Macond | CC BY-SA 3.0 |