- Sep 29, 2012
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Re: Re:
You should see Ed Coyle's paper on efficiency based on Lance Armstrong. That's filled with far worse crapola than only having 11 samples.
WillemS said:acoggan said:ScienceIsCool said:There's a strong inverse relationship between economy (efficiency) and VO2max as measured for a dozen world-class cyclists.
I wouldn't consider an R2 of only 0.41 to be "strong".
Interpretation of the coefficient of determination is actually largely dependent on the context, in some cases a R² of .10 is impressive, while in other situations you're only going to be satisfied with your model if you found a R² of over .90. As we're dealing with physiological data and phenomena that are probably affected by multiple factors, I feel that finding such a coefficient of determination in a bivariate relationship is actually quite impressive. However, in the context we're discussing the matter, we should be warned that, in the sample of that study, there's still .59 (59% of the variance) left that you cannot account for using the relationship between VO2max and Gross Efficiency.
However, more importantly, R² is a sample statistic and the Pearson product moment correlation coefficient is only a point-estimate of the population correlation parameter. Given the low sample size (11) and relatively large standard error (0.25), the actual population parameter for the correlation may differ quite a bit from the value obtained in this sample. As the results section of the paper is severely lacking, I've reanalysed the data using the reported raw data to calculate a confidence interval for the correlation. While my correlation coefficient (-.66) is somewhat different from one reported in the paper (-.64), probably due to the fact the authors rounded the raw data to one decimal, the 95% Confidence Interval for Rho, calculated using the Fisher z' transformation method, is quite wide: 95% CI [-0.901,-0.094]. This indicates that we should not hold too much to exact value of the point-estimate of -.66 (-.64 in the paper), as it may be quite unstable over different samples. To get a more accurate or narrow estimate of the population correlation, we need more data points.
You should see Ed Coyle's paper on efficiency based on Lance Armstrong. That's filled with far worse crapola than only having 11 samples.
