Summary

If you do not want to read through the entire article:

Based on the simulations presented, in my opinion, the best way to handle errors calculated from replicates of experiments which involve fitting the data is the following:

• Fit the data from each replicate independently.
• Take the mean of the estimates for the fitted values (here - k values, \(\bar{k}\)) obtained from each fit.
• Calculate the standard error of the mean for \(\bar{k} \;\) (\(SEM(\bar{k})\)).
• Propagate the standard error of fit to arrive at a fitting error for \(\bar{k} \;\) (\(\sigma_{fit}(\bar{k})\)).
• Combine the errors by squaring them, summing them and taking the square root (\(\sigma_{tot}(\bar{k}) = \sqrt{(\sigma_{fit}(\bar{k}))^2 + (SEM(\bar{k}))^2}\)), thus arriving at a final value for k with quantified uncertainty (\(\bar{k} \pm \sigma_{tot}(\bar{k})\)).

The presented simulations show that a random effects model also is also effective. However, for the vast majority of chemists/wet lab scientists (?) interested in appropriately accounting for error as assessed by repeated measurements, the above workflow should be sufficient in the majority of cases.