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Table 1 Multi-level regression analyses for the changes in running speed of the annual ten fastest female and male age group finishers across years in 100 km and 100 miles after correction for multiple finishes and age of athletes with multiple finishes

From: Age group performances in 100 km and 100 miles ultra-marathons

  ß p Trend of the change across years
100 km women    
25–29 years 0.015 0.167 no change
30–34 years 0.070 < 0.001 non-linear polynomial regression 5th degree
35–39 years 0.051 < 0.001 non-linear polynomial regression 5th degree
40–44 years 0.056 < 0.001 non-linear polynomial regression 5th degree
45–49 years 0.031 < 0.001 non-linear polynomial regression 4th degree
50–54 years 0.027 < 0.001 non-linear polynomial regression 5th degree
55–59 years 0.098 < 0.001 non-linear polynomial regression 3rd degree
60–64 years 0.098 < 0.001 linear
100 km men    
18–24 years 0.056 < 0.001 non-linear polynomial regression 5th degree
25–29 years 0.085 < 0.001 non-linear polynomial regression 6th degree
30–34 years 0.068 < 0.001 non-linear polynomial regression 4th degree
35–39 years 0.077 < 0.001 non-linear polynomial regression 4th degree
40–44 years 0.089 < 0.001 non-linear polynomial regression 4th degree
45–49 years 0.092 < 0.001 non-linear polynomial regression 4th degree
50–54 years 0.092 < 0.001 non-linear polynomial regression 4th degree
55–59 years 0.076 < 0.001 non-linear polynomial regression 4th degree
60–64 years 0.041 < 0.001 non-linear polynomial regression 4th degree
65–69 years 0.104 < 0.001 linear
70–74 years 0.088 < 0.001 linear
75–79 years 0.107 < 0.001 linear
100 miles women    
25–29 years 0.175 < 0.001 linear
30–34 years 0.090 < 0.001 linear
35–39 years 0.091 < 0.001 non-linear polynomial regression 3rd degree
40–44 years 0.074 < 0.001 non-linear polynomial regression 3rd degree
45–49 years 0.093 < 0.001 non-linear polynomial regression 4th degree
50–54 years 0.094 < 0.001 linear
55–59 years 0.052 0.005 linear
100 miles men    
18–24 years 0.199 < 0.001 linear
25–29 years 0.057 < 0.001 non-linear polynomial regression 5th degree
30–34 years 0.064 < 0.001 non-linear polynomial regression 4th degree
35–39 years 0.070 < 0.001 non-linear polynomial regression 4th degree
40–44 years 0.097 < 0.001 non-linear polynomial regression 5th degree
45–49 years 0.082 < 0.001 non-linear polynomial regression 4th degree
50–54 years 0.069 < 0.001 linear
55–59 years 0.068 < 0.001 linear
60–64 years 0.051 < 0.001 linear
65–69 years 0.087 < 0.001 linear
  1. The trend of the regression (linear or non-linear) is also inserted.