## 2 Oxygen Phosphoric Acid Fractionation Factor for Low-Mg Calcite: Data and Discussion  
### Selection of Data at Different Temperatures  
Many important papers report data of \(\alpha_{\mathrm{ACID(\theta)}}^{\mathrm{T}}\) for carbonate minerals and/or of \(\delta^{18}\mathrm{O}_{\mathrm{CO2(\Theta)}}^{\mathrm{T}}\) at different temperatures (e.g., [4; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]; for a list of \(\alpha_{\mathrm{CO}_{2}-\theta}^{298.15}\) estimated values see [17]). Among these data, we selected some values for low-Mg calcite according to the following two criteria:  
1. Only data sets that include values for more than two analytical temperatures were considered and compared. 2. We considered only data obtained with the individual-acid bath method (IAB). Unfortunately, the authors frequently do not report single data, but averages at different temperatures, which reduces the statistical information. For this reason, we were compelled to use averages instead of single data (with the exception of Calcite H\({}^{(1)}\) in Table 1). Some of the cited works demonstrate the low analytical repeatability of the fractionation factor determination at 25 \({}^{\circ}\)C (e.g., [13; 15]). [PERSON] et al. [15] report a spread of data that is larger at 25 \({}^{\circ}\)C than at higher temperature. These authors use the \(\delta^{13}\mathrm{C_{CAL/PDB}}\) values for the selection of the oxygen data on low-Mg calcite. Given a defined sample, they consider the average \(\bar{\delta}\,^{13}\mathrm{C_{CAL/PDB}}\)\(\pm\) standard deviation = \(-4.62\%\)\(\pm\) 0.06% for the carbon isotopes and eliminate the corresponding \(\delta^{18}\mathrm{O_{CO_{2}(CAL)/PDB}^{T}}\) value in case the sample is \(10^{3}|\delta^{13}\mathrm{C_{CAL/PDB}}-\bar{\delta}^{13}\mathrm{C_{CAL/PDB}}|\) > 0.06. This drastic method is very \"efficient\", although not typical for the identification of aberrant values. We prefer to consider all the data for the reasons listed below. Firstly, regarding elimination of data we follow the [PERSON]'s golden rule [18]: \"No value should be removed from a data set on statistical ground alone\" (p. 20) and \"Delete extreme values only when a technical reason for their aberrant behavior can be found\" (p. 23). Additionally, in case this opinion is not accepted, only data with very low probability of occurrence (indicatively with probability less than 0.05 or 0.01) should be eliminated. The carbon \(\delta^{13}\mathrm{C}\) data reported by [PERSON] et al. [15] have abnormal distribution (Shapiro-Wilk test: \(\mathrm{P_{normal}}\) = 0.014). In this case, the standard deviation of the statistical sample does not express the spread of the data around the central value in the right way. In the case that the distribution is not normal, the use of simple non-parametric methods is suggested. For instance, the box and whiskers plot [19] indicates that no one value from [PERSON] et al. 's data [15] for calcite is an \"outlier\". Estimation of Oxygen Isotope Phosphoric Acid Fractionation Factor, \(\alpha_{ACID(CAL)}^{\mathrm{T}}\), at 298.15 K  
Using the estimated values reported by the authors, we verified that the linear relation between the data \(\alpha_{\mathrm{ACID(\Theta)}}^{\mathrm{T}}\) vs T\({}^{-2}\) (in kelvin when not indicated otherwise) generally gave lower standard error of regression than vs T\({}^{-1}\).