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I have a experimental physics/statistical dilemma, mainly related to the uncertainty determination of the Plasma Electron Temperature when determined experimentally with a Langmuir Probe.

So the electron current model is given by

$$I_{e}(V_{b})=I_{e}^{\textrm{sat}}\cdot\exp{\left(\frac{V_{b}-V_{s}}{T_{eV}}\right)}$$

Where $I_{e}(V_{b})$ is the current measured when a bias potential $V_{b}$ is applied to the probe's tip. From the linearization of the electron current data, when a linear least-squares fit is applied the slope would be $1/T_{eV}$.

The Least-squares regression method has a way to determine the standard error associated to the slope $1/T_{eV}$, but, how can it be taken into account when multiple $1/T_{eV}$ are determined, so that the best uncertainty is estimated.

Roger V.
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Allan J. González Villalobos
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  • I do not understand your last comment/question about multiple electron temperatures being measured to determine the best uncertainty. As for a least-squares fit, https://en.wikipedia.org/wiki/Least_squares has a decent explanation of the method and uncertainty calculation. – honeste_vivere Nov 29 '21 at 13:56
  • Hi, that's right, but that method does not take into account the repeatibility of the parameter you get from every dataset of each experiment. – Allan J. González Villalobos Nov 29 '21 at 22:24
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    You might want to like into this question: https://physics.stackexchange.com/questions/679853/how-to-calculate-the-uncertainty-and-mean-of-multiple-measurements-with-differen – Semoi Nov 30 '21 at 19:59
  • Hey, thanks! This definitely helps, I'll look for the reference. – Allan J. González Villalobos Dec 01 '21 at 19:48

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