Accuracy of SRM and power tap power monitoring systems for bicycling

Purpose: Although manufacturers of bicycle power monitoring devices SRM and Power Tap (PT) claim accuracy to within 2.5%, there are limited scientific data available in support. The purpose of this investigation was to assess the accuracy of SRM and PT under different conditions. Methods: First, 19 SRM were calibrated, raced for 11 months, and retested using a dynamic CALRIG (50-1000 W at 100 rpm). Second, using the same procedure, five PT were repeat tested on alternate days. Third, the most accurate SRM and PT were tested for the influence of cadence (60, 80, 100, 120 rpm), temperature (8 and 21degreesC) and time (1 h at similar to300 W) on accuracy. Finally, the same SRM and PT were downloaded and compared after random cadence and gear surges using the CALRIG and on a training ride. Results: The mean error scores for SRM and PT factory calibration over a range of 50-1000 W were 2.3 +/- 4.9% and -2.5 +/- 0.5%, respectively. A second set of trials provided stable results for 15 calibrated SRM after 11 months (-0.8 +/- 1.7%), and follow-up testing of all PT units confirmed these findings (-2.7 +/- 0.1%). Accuracy for SRM and PT was not largely influenced by time and cadence; however. power output readings were noticeably influenced by temperature (5.2% for SRM and 8.4% for PT). During field trials, SRM average and max power were 4.8% and 7.3% lower, respectively, compared with PT. Conclusions: When operated according to manufacturers instructions, both SRM and PT offer the coach, athlete, and sport scientist the ability to accurately monitor power output in the lab and the field. Calibration procedures matching performance tests (duration, power, cadence, and temperature) are, however, advised as the error associated with each unit may vary.

Zero-non-zero patterned vector error correction modeling for I(2) cointegrated time series with applications in testing PPP and stock market relationships

Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero entries in all their coefficient matrices. However, applications of VECM models to financial market data have revealed that zero entries are often a necessary part of efficient modelling. In such cases, the use of full-order VECM models may lead to incorrect inferences. Specifically, if indirect causality or Granger non-causality exists among the variables, the use of over-parameterised full-order VECM models may weaken the power of statistical inference. In this paper, it is argued that the zero–non-zero (ZNZ) patterned VECM is a more straightforward and effective means of testing for both indirect causality and Granger non-causality. For a ZNZ patterned VECM framework for time series of integrated order two, we provide a new algorithm to select cointegrating and loading vectors that can contain zero entries. Two case studies are used to demonstrate the usefulness of the algorithm in tests of purchasing power parity and a three-variable system involving the stock market.

Comparative phylogeographic summary statistics for testing simultaneous vicariance

Testing for simultaneous vicariance across comparative phylogeographic data sets is a notoriously difficult problem hindered by mutational variance, the coalescent variance, and variability across pairs of sister taxa in parameters that affect genetic divergence. We simulate vicariance to characterize the behaviour of several commonly used summary statistics across a range of divergence times, and to characterize this behaviour in comparative phylogeographic datasets having multiple taxon-pairs. We found Tajima's D to be relatively uncorrelated with other summary statistics across divergence times, and using simple hypothesis testing of simultaneous vicariance given variable population sizes, we counter-intuitively found that the variance across taxon pairs in Nei and Li's net nucleotide divergence (pi(net)), a common measure of population divergence, is often inferior to using the variance in Tajima's D across taxon pairs as a test statistic to distinguish ancient simultaneous vicariance from variable vicariance histories. The opposite and more intuitive pattern is found for testing more recent simultaneous vicariance, and overall we found that depending on the timing of vicariance, one of these two test statistics can achieve high statistical power for rejecting simultaneous vicariance, given a reasonable number of intron loci (> 5 loci, 400 bp) and a range of conditions. These results suggest that components of these two composite summary statistics should be used in future simulation-based methods which can simultaneously use a pool of summary statistics to test comparative the phylogeographic hypotheses we consider here.