Timeline for How can I calculate uncertainty of the mean of a set of samples with different uncertainties?
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| Mar 15, 2020 at 20:38 | comment | added | whuber♦ | I agree that if the measurement SDs were obtained from repeated measurements, then it would be ideal to have the original measurements. The appropriate analysis in this case is a components of variance analysis, carried out using ANOVA machinery. However, note that if we only had (a) the number of measurements in each case and (b) an indication of exactly how the $\pm$ values were computed then that would suffice to do all the necessary calculations. | |
| Mar 15, 2020 at 18:07 | comment | added | George Sotiropoulos | @whuber Ideally you need the original measurements. I guess that those errors come from some tests which also have a distribution. | |
| Mar 15, 2020 at 18:01 | comment | added | user32398 | The OP never gave the same size, so there is nothing wrong with this answer which suggests a simulation using 1000 realizations - purely Monte Carlo uncertainty analysis. In fact, you could use 10,000 realizations. Standard deviation doesn't change with sample size, but power depends on effect size, sample size, and significance. I don't recommend (other comment) turning the OP into a power and sample size question. | |
| Mar 15, 2020 at 17:29 | comment | added | whuber♦ | This proposal is erroneous because the testing will be applied to a much larger dataset than is actually available. In particular, p-values in the t-test will be far too small and standard errors of the mean will be far too narrow. | |
| Mar 15, 2020 at 16:03 | history | answered | George Sotiropoulos | CC BY-SA 4.0 |