Critical speed estimated by statistically appropriate fitting procedures

Intensity domains are recommended when prescribing exercise. The distinction between heavy and severe domains is made by the critical speed (CS), therefore requiring a mathematically accurate estimation of CS. The different model variants (distance versus time, running speed versus time, time versus running speed, and distance versus running speed) are mathematically equivalent. Nevertheless, error minimization along the correct axis is important to estimate CS and the distance that can be run above CS (d'). We hypothesized that comparing statistically appropriate fitting procedures, which minimize the error along the axis corresponding to the properly identified dependent variable, should provide similar estimations of CS and d' but that different estimations should be obtained when comparing statistically appropriate and inappropriate fitting procedure.

Sixteen male runners performed a maximal incremental aerobic test and four exhaustive runs at 90, 100, 110, and 120% of their peak speed on a treadmill. Several fitting procedures (a combination of a two-parameter model variant and regression analysis: weighted least square) were used to estimate CS and d'.

Systematic biases (P < 0.001) were observed between each pair of fitting procedures for CS and d', even when comparing two statistically appropriate fitting procedures, though negligible, thus corroborating the hypothesis.

The differences suggest that a statistically appropriate fitting procedure should be chosen beforehand by the researcher. This is also important for coaches that need to prescribe training sessions to their athletes based on exercise intensity, and their choice should be maintained over the running seasons.