Cross-validation of Equations for Estimating Pre-training, Post-training, and Training-induced Changes in Leg Extension 1-Repetition Maximum

Trevor D. Roberts^1, , Robert W. Smith², Jocelyn E. Arnett¹, Dolores G. Ortega¹, Justin S. Pioske¹, Richard J. Schmidt¹ and Terry J. Housh¹

¹Department of Nutrition and Health Sciences, University of Nebraska-Lincoln, Lincoln, NE 68583, USA

²Department of Health, Human Performance, and Sport, Wayne State College, Wayne, NE 68787, USA

Cite this paper:
Trevor D. Roberts, Robert W. Smith, Jocelyn E. Arnett, Dolores G. Ortega, Justin S. Pioske, Richard J. Schmidt and Terry J. Housh. Cross-validation of Equations for Estimating Pre-training, Post-training, and Training-induced Changes in Leg Extension 1-Repetition Maximum. American Journal of Sports Science and Medicine. 2024; 12(2):29-35. doi: 10.12691/ajssm-12-2-2

Abstract

Eight previously published equations (EQs) that estimate 1-repetition maximum (1-RM) from repetitions to failure (RTF) were cross-validated for estimating pre-training, post-training, and training-induced changes (post-training minus pre-training) in leg extension (Leg Ext) 1-RM. Thirty-one recreationally active men (age: 20.8±1.5 years; body mass: 81.7±14.6 kg) trained 3 days per week for 8 weeks with 1 bilateral Leg Ext set to failure at ~80% 1-RM. The subjects performed Leg Ext 1-RM and RTF tests at pre-training and post-training. The pre-training and post-training RTF were performed at ~80% pre-training 1-RM and the values were input into the EQs for estimating the 1-RM values. The measured changes in 1-RM and RTF from pre-training to post-training were analyzed with paired t-tests. The cross-validation statistical analyses included paired t-tests for the constant error, correlation coefficient, standard error of the estimate, and total error (TE). Training significantly increased (p < 0.001) Leg Ext 1-RM (pre-training: 126.9±25.2 kg; post-training: 161.6±24.6 kg) and RTF (pre-training: 9.8±2.7 repetitions; post-training: 19.9±7.6 repetitions) by 34.6 kg and 10.1 repetitions, respectively. The cross-validation analyses indicated that an exponential EQ (Estimated 1-RM = RTF^0.1•weight lifted) exhibited the lowest TE (3.9 kg) for estimating pre-training 1-RM, however, all EQs exhibited high TE values for estimating post-training 1-RM (21.9 to 606.3 kg) and changes in 1-RM values (24.0 to 603.1 kg) relative to the mean measured values of 161.5 kg and 34.6 kg, respectively. Therefore, this exponential EQ is recommended for estimating a pre-training Leg Ext 1-RM with 4 to 17 RTF in recreationally active men, but none of the EQs in the present study are recommended for estimating post-training Leg Ext 1-RM or changes in Leg Ext 1-RM values with post-training RTF ranging from 11 to 37 RTF.

Keywords:
prediction error accuracy muscular strength resistance training repetitions to failure

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