Should I average data sets and calculate single parameter or average individual data set's parameters? I am interested in calculating oxidation reaction kinetics parameters of a material at a particular temperature. Essentially I have a curve of data (mass change) vs. time for the particular temperature. I have repeated the experiment three times so I have three individual curves. Technically each of these curves should be the exact same, and the calculations of their curve's parameters (such as slope) should result in the same values. However, experimental variance causes the curves and their respective parameters to have slightly different values.
I am wondering if there is any mathematical difference between averaging the curves of data and calculating a single parameter from the single averaged curve (that parameter would have a C.I. determined from regression of the parameter), vs. calculating individual parameters for each individual curve and then finding the average and C.I. of the set of those three parameters/curves?
I have been trying to obtain some insight into this, but I cannot seem to figure out the proper phrasing to search google effectively.
 A: As I understand your question, you have done 3 separate experiments under the same conditions, each time fitting a model of the change of sample weight over time at fixed temperature to obtain estimates of the model parameter values. Your question is whether you should average the parameter values among the 3 separate analyses or to average the curves first and then determine the parameter values from the averaged curve.
The correct answer, as implied by the comment from @Glen_b, is neither of those. The best approach will generally be to use all the data points individually, without prior averaging, together in a combined analysis, while taking into account the experiment from which each data point was derived.
The errors of estimates of parameter values depend on the residual degrees of freedom in the analysis, typically the number of data points minus the number of estimated parameter values. As a rule of thumb, you might expect the precision (reciprocal of error) to be proportional to the square root of the number of degrees of freedom.
So if you do 3 experiments each with $N$ observations and estimate $P$ parameter values from all $3N$ data points, then the precision is proportional to $\sqrt{3N-P}$.
For each experiment analyzed separately the precision would be lower, proportional to $\sqrt{N-P}$. Averaging the values over 3 experiments would somewhat improve the precision by a factor of $\sqrt{3}$, with a net result for precision proportional to $\sqrt{3N-3P}$. That is lower precision than for the pooled analysis.
Working simply with the averaged curves would improve the precision at each individual time point by a factor of $\sqrt{3}$, but you are now using only $N$ (averaged) data values to estimate $P$ parameter values, so you are have roughly the same (poor) precision as for averaging the 3 parameter-value estimates.
The above only holds, however, if there were no substantial systematic differences among the 3 experiments. So you should let your data tell you how to proceed. 
The trick is to include an experiment identifier along with each separate data point, and then do an analysis of variance to determine whether there is a significant difference among the experiments. There is an example of how to do this with nonlinear curve fitting in R on this page; see under the heading of "Comparing fits to different data sets" and the associated R code farther down the page.
If there are no significant differences among experiments (or the differences are too small to be of practical importance even if they are "significantly different" due to very high inherent precision or large numbers of observations), then the estimates from pooled analysis will be best. If there are substantial differences among the 3 experiments, then you perhaps shouldn't be averaging in any way and you should explore why nominally identical experiments gave different results.
