The long-distance events have been held at the Olympic Games since 1908. The 1500 m event has always been a men��s event. The 1986 Olympic Games mark the beginning of women��s 800 m races. PF-01367338 Statistical analysis In order to analyse the improvement in athletes�� performance in a given freestyle event, each time the constant-base and variable-base indices were calculated for the results of eight Olympic Games finalists, while the trend function was selected afterwards. Because a time-series model is a descriptive dynamic model (i.e. one omitting the causes of the course of the analysed phenomenon), the constructed models were verified by testing the significance of the structural parameters (the t-Student test) and the randomness of residuals, as well as the error term autocorrelation (the Durbin-Watson test).
The coefficients of convergence indicating the goodness-of-fit between the constructed models and the empirical data were calculated for all swimming events. Swimmers�� performances at the 2012 Olympic Games in London were predicted using the moving average method and linear and non-linear regressions. The regression models�� goodness-of-fit was estimated with the coefficient of determination. Results 50 m freestyle The data used to produce Graph 1 reveal that the times of both male and female swimmers tend to improve. This tendency is not constant, though, as indicated by their slight regression at the 1996 Olympic Games in Atlanta, amounting to 1.5% for women and 1.6% for men. During the 20 analysed years the eight female and male finalists examined here improved their results, on average, by 1.
55 s (6.0%) and 1.28 s (5.5%), respectively. Another interesting finding is that women��s results were systematically moving closer to men��s, as confirmed by the differences between the average women��s and men��s times recorded at the Seoul Olympic Games (3.01 s ) and in Beijing (2.75 s). Moreover, the men��s performance curve plotted in the graph clearly shows that the finalists�� results tend to concentrate, which follows from the rising level of athletic performance, as well as from the growing competition among elite sprint swimmers. Graph 1 Women��s and men��s performances in the 50 m freestyle during the 6 past Olympic Games and the prediction for London 2012 The next step in the analysis was an attempt to predict the results for the upcoming Olympic Games.
The trend function was selected based on moving averages and then its goodness-of-fit to the empirical data was determined. The coefficients of convergence 2 were Brefeldin_A 0.11 and 0.06 for women and men, respectively, thus proving that the goodness-of-fit between the linear trend function and the empirical data was very high �C the trend function could not explain only 11.0% and 6.0% of variability in athletes�� performance. Therefore, because the trend function was defined well, the probable times of the female and male finalists may be 24.15 s and 21.46 s, respectively.