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In this paper Pitman's asymptotic efficiency (AE) as well as Kallenberg's intermediate AE of the goodnessof-fit tests based on higher-order non-overlapping spacings is considered. We study log statistic as well as entropy type statistic based on k-spacings when k may tend to infinity as n approaches infinity. It certainly compliments the available results for fixed k and provides more general result. We show that both types of statistics based on higher ordered spacings have higher efficienciesdoi:10.18187/pjsor.v14i4.1951 fatcat:c4nwlibvmvep5oioiuivoxxmjy