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Cramer, Joel T. PhD, FACSM; Ryan, Eric D. PhD

Medicine & Science in Sports & Exercise: February 2009 - Volume 41 - Issue 2 - p 480
doi: 10.1249/MSS.0b013e318191476c
SPECIAL COMMUNICATIONS: Letters to the Editor-in-Chief

Biophysics Laboratory, Department of Health and Exercise Sciences, University of Oklahoma, Norman, OK

Dear Editor-in-Chief:

First, we would like to thank you for allowing us to respond to Dr. Knudson's comments. Second, we wish to thank Dr. Knudson for his interest in our paper and acknowledge our respect for his contributions to the literature on this topic (6-8).

Dr. Knudson's first concern was that we did not acknowledge his previous study (7), two studies that were published while ours was in press (5,10), an abstract (9), and a paper by Brandenburg (1). However, none of the studies cited by Dr. Knudson (1,5,7,9,10) involved the plantar flexors or the twitch interpolation technique; therefore, these studies were not directly related to our experimental approach.

Dr. Knudson's second concern was that our study was underpowered because of a sample size of n = 13. Our observed statistical power values for the omnibus F statistics in the ANOVA models for each of our dependent variables (peak torque, range of motion, peak twitch torque, rate of torque development, EMG amplitude, and percent voluntary activation) were 0.75, 1.00, 0.88, 0.95, 0.76, and 0.65, respectively. We would consider these power values acceptable and high enough to detect a statistical difference if there was one. Furthermore, the goal of our study was to extend the findings of Fowles et al. (2) and other studies (4,13) on the plantar flexors, which each had sample sizes of n = 10, n = 15, and n = 15, respectively. We believe our sample size of n = 13 was consistent with these studies.

Dr. Knudson's third concern was his recommendation to correct for Type I error inflation. Such statistical adjustments of the alpha level, such as the Bonferroni correction, are typically reserved for multiple ANOVA or t-tests on a single dependent variable (12). We used the highest-order ANOVA, which was also the most powerful univariate ANOVA model (12) that was possible for each of our six dependent variables. Therefore, we would argue that no such correction was necessary. In addition, when reducing the alpha level to widen the confidence interval as suggested by Dr. Knudson, there is an increased risk of a Type II error (3), which occurs when the study fails to detect differences that really do exist (12). Therefore, our 95% confidence interval (α = 0.05) combined with the observed statistical power values in the present study suggested that if there was a significant stretching-induced force deficit beyond the control condition, we would have detected it.

In conclusion, we agree with Dr. Knudson's suggestion that not only our study (11) but also all original research studies should be evaluated with caution.

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