In this paper a single-factor analysis of variance (ANOVA) is described and applied. The task of the method is to determine whether the observed factor has influence to the output variables or parameters of the observed system. In order to apply the ANOVA method, certain assumptions should be valid, such as the homogenity of variance standardly tested by the Levene test, which is described and applied. When the assumption of homogenity of variance is violated, instead of the classical ANOVA method the Welch ANOVA test is used. When ANOVA indicates that the difference between treatment means exist, the post-hoc tests are applied to determine where this difference appears. The ANOVA method was practically implemented in the Python software package on cyclic and fatigue parameters data of different groups of steels: nonalloyed, lowalloyed and high-alloyed. The obtained results suggest that for all observed parameters there exist statistically significant differences with respect to the steel group. Using the Tukey test, a post-hoc analysis was also performed to determine exactly for which group of steels there exist differences in the parameter values. Finally, some additional methods of multiple comparisons are listed and possible extensions of one-factor ANOVA to cases when there is an influence of several different factors on the system parameters are briefly described.