Problems associates with the analysis of the pattern of total cross-country eventing penalty scores at advanced level of competition in the United Kingdom

Eventing is a three phased equestrian sport. It involves the competition of a dressage test, round of show jumps and completion of a cross-country course. The cross-country phase is described by the sports governing body as the most important and influential element of the competition. Within the sport various levels of competition are run and equality of competition should be maintained at within these levels. The paper compares the relative effect of the cross-country phase of competition between 10 advanced events (sub populations) run in during 2003. Non-normality was apparent within the whole population (Kolmogorv Smirnov K statistic = 5.178 (p<0.001); Shapiro Wilks W = 0.711 (P<0.001). The use of Log (x+1) transformation was applied, positive skew (+2.853) was reduced after transformation to −0.543 (Kolmogorov K statistic = 0.754; p>0.05). The influence of extreme kurtosis was removed after transformation (+10.581 reduced to +1.288). The paper suggests that there is considerable variation observed between some sub populations. Measures of central tendency are discussed as comparative measures between events. It is apparent that arithmetic means may be misleading and the uses of other measures of central tendency are discussed including maximum likelihood estimators. Analysis of data distribution using box and whisker plots indicated outliers and extreme outliers were exerting a considerable effect on the population.