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We show that, within the family of power transformations of a Chisquare variable, the square and fourth roots m i n i z e Pearson's index of kurtosis. Two new transtormations of the fourth root, a symmetrized-truncated version and its linear combination with the square root are also studied. The first transformation shows a considerable improvement over the fourth root while the second one turns out to be even more accurate than Hilferty-Wilson's cube root transformation.

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Summary Here the parametric as well as the non parametric approach to the two‐sample location‐scale problem are reviewed. Special attention is paid to the quadratic form of the linear rank statistics for the location and the scale suggested by Lepage for testing this problem. Several such quadratic forms are compared through ARE computations.

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