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Within the bounds of a general theory of rank correlation two particular measures have been adopted widely: Spearman's rank correlation coefficient, ρ, in which ranks replace variates in Pearson's product-moment correlation calculation; and Kendall's τ, in which the disarray of x-ordered data due to a y-ordering is measured by counting the minimum number, s, of transpositions (interchanges between adjacent ranks) of the y-ordering sufficient to recover the x-ordering. Based on insights from the calculation of Kendall's coefficient, this paper develops a graphical approach which leads to a new rank correlation coefficient akin to that of Spearman. This measure appears to stand outside general theory but has greater power of discrimination amongst differing reorderings of the data whilst simultaneously being strongly correlated with both ρ and τ. The development is focused on situations where agreement over ordering is more important for top place getters than for those lower down the order as, for example, in subjectively judged Olympic events such as ice skating. The basic properties of the proposed coefficient are identified.

This paper analyses a set of world records in athletic running events to extract long-term bounds for those events. The approach adopted is to identify a single parameter to represent the achieved standard of athletic performance at a series of fixed intervals. The long-term behaviour of this single parameter is then investigated by fitting a variety of nonlinear models and restrictions on the accuracy of the fits are discussed. The paper concludes with a range of estimates for each of the events considered in the original data set.

Studies of kurtosis often concentrate on only symmetric distributions. This paper identifies a process through which the standardized measure of kurtosis based on the fourth moment about the mean can be written in terms of two parts: (i) an irreducible component, about L 4 , which can be seen to occur naturally in the analysis of fourth moments; (ii) terms that depend only on moments of lower order, in particular including the effects of asymmetry attached to the third moment about the mean. This separation of the effect of skewness allows definition of an improved measure of kurtosis. This paper calculates and discusses examples of the new measure of kurtosis for a range of standard distributions.

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