## Errors of the derived values

For application in geothermobarometry it is essential to estimate the
errors associated with the derived enthalpies and entropies. The least squares
logic itself provides an estimate of the uncertainties for the values of
enthalpy and entropy through the covariance matrix. This approach was used
by Powell & Holland (1985)
and Holland & Powell (1985, 1990).
However this approach does not seem to be appropriate for the procedure
used here. The resulting errors which the covariance matrix delivers are
dependent on the input parameters. The closer the input parameters are to
a final result, the smaller will be the calculated errors using the covariance
matrix. In the iterative approach used here, the input data were already
relatively close to the final result, making errors calculated from the
covariance matrix meaningless.

To get at least some idea about the confidence of the extracted *Δ**f**H*°
and *S*° values, errors were estimated
using a Monte Carlo simulation, with a variance assigned to each input parameter
of the final iteration. Values within this selected range had to be still
feasible with respect to the experimental results for each mineral reaction
and the calorimetric results. Values within this range were then selected
randomly using a gaussian distribution. With these randomly chosen input
parameters the regression was calculated again. This procedure was repeated
1000 times, every time using a new randomly chosen set of input parameters.
Results were then averaged and the standard deviation (*σ*)
calculated. It is clear that while the resulting errors reflect the assigned
variance of the input parameters, it at least gives some level of confidence
for the extracted *Δ**f**H*° and *S*°.

last modified: 26.11.2008 by Matthias
Gottschalk