# DeltaCC12

ΔCC_{1/2} is a quantity that detects datasets/frames which are non-isomorphous. As described in Assmann and Diederichs (2016), ΔCC_{1/2} is calculated with the σ-τ method. This method is a way to calculate the Pearson correlation coefficient for the special case of two sets of values (intensities) that randomly deviate from their true values. The σ-τ method is not influenced by a random number sequence as shown in Karplus and Diederichs (2012). For the σ-τ method CC_{1/2} is calculated for all datasets/frames, which will be called CC_{1/2_overall} and CC_{1/2} is calculated for all datasets/frames except for one dataset i, which is omitted from calculations and denoted as CC_{1/2_i}. The difference of the two quantities is ΔCC_{1/2}.

- [math]\Delta CC_{1/2}= CC_{1/2 overall}-CC_{1/2\_i} [/math]

If ΔCC_{1/2} is > 0 (CC_{1/2_overall} is bigger than CC_{1/2_i}) it means that by omitting dataset i from calculations a lower CC_{1/2} results. As we want to maximize CC_{1/2} the dataset is kept for calculations, it is improving the whole merged dataset. If Δ CC_{1/2} is < 0 (CC_{1/2_overall} is smaller than CC_{1/2_i}) it means that by omitting dataset i from calculations a higher CC_{1/2} results, which is why we want to exclude it from calculations, because it is impairing the whole merged dataset.

## Applications

The ΔCC_{1/2} method is applicable for single frames, SSX data and SFX data. The program XDSCC12 calculates ΔCC_{1/2} for the isomorphous and anomalous signal for XDS_ASCII.HKL and XSCALE.HKL files. Exact description of calculation and implementation are found at CC1/2.