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In order to obtain a statistical interpretation of completeness of a sufficient statistic T, an attempt is made to characterize this property as equivalent to the condition that all ancillary statistics are independent ofT. For technical reasons, this characterization is not correct, but two correct versions are obtained in Section 3 by modifying either the definition of ancillarity or of completeness. The light this throws on the meaning of completeness is discussed in Section 4. Finally,doi:10.1080/01621459.1981.10477652 fatcat:odvmp6izv5asrnbcduhpn2krkm