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The probability formulas given in Parts I and II of this series have been improved by incorporating the information contained in Sim's distribution. Possible applications to the discrimination of the phase ambiguities arising from the single isomorphous replacement technique, the one-wavelength anomalous scattering (OAS) technique or pseudo centrosymmetry in small structures are discussed. With a set of experimental protein OAS data, the efficiency of the improved formula has been shown to be better than that of the older one.
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