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I have a best-estimate value for some quantity $H$, along with uncertainty $\delta H$. I am told that the best-estimate $H$ was determined by fitting some unknown function involving $H$ and an arbitrary number $n$ of other parameters, $g(H; x_0...x_n)$, to a set of data. $H$ is thus the resultant best-fit parameter with uncertainty $\delta H$. I am also given the reduced sum of square deviations of the data to the fitting function the determined $H$, $\chi^2$.

This is all I know. I do not have the raw data that was fit to, nor how many points were used in the fit. All I have is

$$H$$ $$\delta H$$ $$\chi^2$$

Using these three pieces of information, is it possible to deduce the statistical significance of the best-estimate value $H$?

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  • $\begingroup$ What exactly does the "uncertainty" $\delta H$ represent? If it can be related to the sampling variance of $H$, and if you can justify specific assumptions about the sampling distribution of $H$, then you can do something. But if either one of these doesn't hold, all bets are off. $\endgroup$
    – whuber ♦
    Commented Jun 21, 2017 at 20:58
  • $\begingroup$ @whuber I've got no idea. I assume it is the standard error in the parameter fit. I $\endgroup$
    – pretzlstyle
    Commented Jun 21, 2017 at 21:21
  • $\begingroup$ That could be a risky assumption, since people report radically different values of "uncertainty": in addition to an SE, it could be two or three SEs, a 50%/90%/95%/99% (or whatever) credible/confidence (half-)interval, or even sometimes the SD of the data from which $H$ was estimated. The first thing, then, is to find out what $\delta H$ actually means. $\endgroup$
    – whuber ♦
    Commented Jun 21, 2017 at 22:06
  • $\begingroup$ @whuber I was able to gather enough information to determine that the data in question is indeed fit with a standard Gaussian form, at least. I'll email the author of this paper as to more details of the error estimate. Even if I do find out this information, is it possible to recover a statistical significance? $\endgroup$
    – pretzlstyle
    Commented Jun 22, 2017 at 16:42

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