The calibration result for each thermocouple was used to correct the offset error and the slope error was propagated to calculate the measurement uncertainty (approximately ±0.2 °C), represented by the x-axis error bars shown in Fig. 4b.
We could estimate the error from the standard error of the slope of the rate regression, but this under-predicts the actual variability of day-to-day replicates.
The statistical methodology for assessment of this hyperbolic relationship is critical when both the x and y variables are measured with error, as the slope will be underestimated if measurement error in the independent variable is not accounted for (23).
The standard error of the y-axis intercept was ± 0.0152 RIF per cell and the standard error of the slope was ± 0.0009 RIF per cell · mGy−1.
This observed slope is not statistically significant, and the error on the slope of ± 0.05% was retained.
The slope of the linear regression at Addis Ababa, Trivandrum, Kakioka, Chambon-La-Foret, and Niemegk was larger than the standard error of the slope.
Hence, for the fourth criterion, the scatter parameter (σ/ǀbǀ; Coe et al., 1978), represented by the standard error of the slope divided by the slope (ǀbǀ), is restricted to ≤0.1.
However, due to the large error in the slope determination, which is partly due to the few points at low conductance, this slope might very well be constant and of about 0.35 for all temperatures.
If the residual error of the slope (|γ j | ≥ 3σ) of the connecting line j of a certain matching points is greater than 3 (standard error), the said matching points can be rejected as mismatching ones (Yang et al. 2014).
Furthermore, no significant correlation with ΔG est) is observed since the relative error of the slope of the regression line is approx. 70% of the slope itself.
