Analyzing Maximal Isometric and Isokinetic Torque in Athletes

The statistical analyses were executed using SPSS Statistics 29 (IBM, Armonk, New York, United States) and Excel (Office 365, Microsoft, Redmond, Washington, United States). Different approaches were used according to the research questions mentioned in the introduction. Basically, all data were normally distributed as confirmed by the Shapiro–Wilk test. Parametric tests were chosen for statistical comparisons (see below). In this case, RM ANOVA was used, and sphericity was checked by Mauchly’s test. In case of significance, the Greenhouse–Geisser correction was applied (F_G). Cohen’s effect size f was given for RM ANOVA, where Cohen’s f was calculated by $\sqrt{\frac{{\eta }^2}{1-{\eta }^2}}$ (Cohen, 1988 ). For t tests (paired or unpaired), Hedges’ effect size g was calculated by SPSS. The effect sizes were interpreted as small (0.2), moderate (0.5), large (0.80), or very large (1.3) (Cohen, 1992 (link); Sullivan and Feinn, 2012 (link)). Significance level was α = 0.05.

1) Behavior of force parameters with respect to repeated AF measurements (n = 12):

The linear mixed model (method: restricted maximum likelihood; REML) was used to investigate the maximal torques regarding time (pre/post or start/end, respectively) and parameter (AF_max, AFiso_max, and MVIC). ‘Time’ and ‘parameters’ were set as fixed factors. Since time*parameter was not found to be significant in terms of fixed factors, it was removed from the mixed model in order to reduce complexity. ‘Subject’ (ID) and ‘parameter’ were defined as random effects for the first estimation. Since ‘parameter’ turned out to be not significant in covariance estimation, consideration of the random factor was not necessary (Baltes-Götz, 2020 ). The Kenward–Roger approximation was used to estimate the degrees of freedom (df) since it provides a better estimation for small sample sizes (Baltes-Götz, 2020 ). This model revealed the best Bayesian information criterion (BIC) and was therefore used.
The ratio of AFiso_max to AF_max was compared between start and end by the paired t-test. Relative declines of parameters from pre to post or start to end (%), respectively, were calculated and compared using the paired t-test for each parameter (one-tailed test for AFiso_max vs. AF_max or MVIC, since AFiso_max was assumed to decrease stronger; two-tailed test for AF_max vs. MVIC).
Slopes of regression lines of the single values of each parameter (AF_max and AFiso_max) regarding the 30 AF measurements (M1–M30) were calculated to describe a possible decline during repetition trials. The paired t-test (one-tailed) was performed to investigate a possible difference between the slopes of AFiso_max and AF_max.
Furthermore, the 30 AF trials were divided into six intervals (I1–I6), which consisted of the arithmetic mean of each five subsequent trials: I1 (M1–M5), I2 (M6–M10), I3 (M11–M15), I4 (M16–M20), I5 (M21–M25), and I6 (M26–M30). RM ANOVAs for every AF parameter considering the six intervals were performed. Pairwise comparisons were executed using the Bonferroni correction (adjusted p-value = p_adj).

2) Comparison of force parameters (n = 12)

The comparison of maxAFiso_max and maxMVICpre is most important regarding the differentiation of HIMA and PIMA. maxAFiso_max and maxAF_max refer to the highest value of all 30 trials regarding AFiso_max and AF_max, respectively. The paired t-test was used to check for differences between the maximal torques.

3) Comparisons between sports groups (endurance vs. strength athletes)

This consideration has to be regarded as preliminary due to the small sample sizes of both groups. Differences regarding the overall maximal torques of MVIC, AF_max, and AFiso_max between endurance and strength athletes were checked by unpaired t-tests (one-tailed) for each parameter separately.
The relative declines (%) of maxMVIC from pre to post and of AF_max and AFiso_max from start to end were calculated and compared between both sports groups using unpaired t-tests (one-tailed).
The slope values of the linear regression line of AF parameters were used to test for differences between endurance and strength athletes by performing unpaired t tests (one-tailed). The comparisons of the slope of regression lines regarding the ratios were considered as well. This should provide information on the assumed different behaviors of athletes with respect to torque relations.
For the six intervals, a REML was executed for AF_max and AFiso_max. Both parameters were considered separately since only the effect of sports types was of interest. ‘Interval’ was regarded as a covariate. Fixed factors were ‘sports’ (endurance and strength), ‘intervals’ (I1–I6), and sports*interval. ‘ID’ and ‘interval’ were set as random factors (unstructured).
Regarding the patterns of decline, the averaged torques of I1 (AF_max and AFiso_max, respectively) were set at 100%, and the values of the subsequent intervals were related to the first value. Differences between strength and endurance athletes were checked by a mixed ANOVA (intervals*sports). In the case of significance, pairwise comparisons were performed.