To the editor
Here we refute claims by Todorov1 and Scott7 that the importance of target direction as an explanatory factor for cortical activity in a regression analysis we performed5 is an ‘artifact’ of a square-root transformation of neural discharge rates. Specifically, it was touted by Scott7 that “squaring [sic] the discharge rate of neurons in order to stabilize the variance … causes a dramatic increase in the percentage of neurons that appear to represent movement direction (from 17% [sic] to 43% in Todorov's model).” The data to which Todorov1 referred concerned the percentages of cells for which a particular variable yielded the highest R2 when used alone in the regression. We re-analyzed these data using the regression analysis we used previously5 but without any transformation of the discharge rate. The results of the two analyses were practically identical, the average absolute difference being only 1.9% ( http://www.nature.com/neuro/web_specials/). However, there was a statistically significant improvement of the regression fit when the square-root transformation was used. The median R2 for the square-root transformed data was 0.5811, as compared to 0.544 for the non-transformed data (P < 0.0001, Wilcoxon's signed-rank test). This was anticipated, because the square-root transformation is expected to make the distribution of counts more symmetrical. This transformation is routinely used when analyzing counts8,9,10, given the commonly highly skewed distribution of such data. Finally, we analyzed the data without any transformation or smoothing. In this case, the agreement with the original analysis was even closer, the average absolute difference being only 0.86%. We conclude that the relationship between neural activity and movement parameters found earlier5 holds irrespective of the specific transformation and/or smoothing used. Finally, while we dealt above with the issue of square-root transformation because of the more general importance of this transformation for analyzing neuronal spike counts, there are also numerous other points raised by Todorov1 which we also dispute, including the force direction/magnitude issue, which we cannot critically discuss due to space limitations.
See “Response to 'One motor cortex, two different views'” by Torodov.
References
Todorov, E. Nat. Neurosci. 4, 391–398 (2000).
Schwartz, A. B. Science 265, 540–542 ( 1994).
Moran, D.W. & Schwartz, A. B. J. Neurophysiol. 82, 2693–2704 (1999).
Kettner, R. E., Schwartz, A. B. & Georgopoulos, A. P. J. Neurosci. 8, 2938– 2947 (1988).
Ashe, J. & Georgopoulos, A. P. Cereb. Cortex 6, 590–600 (1994).
Fu, Q.-G., Flament, D., Coltz, J. D. & Ebner, T. J. J. Neurophysiol. 73, 836–854 (1995).
Scott, S. Nat. Neurosci. 4, 307–308 (2000).
Snedecor, G. W. & Cochran, W. G. Statistical Methods (Iowa State Univ. Press, Ames, Iowa, 1989).
Cox, D. R. & Lewis, P. A. W. The Statistical Analysis of Series of Events (Chapman and Hall, London, 1966).
Tukey, J. W. Exploratory Data Analysis (Addison-Wesley, Reading, Massachusetts, 1977).
Rack, P. & Westbury, D. J. Physiol. (Lond.) 204, 443–460 (1969).
Brown, I., Cheng, E. & Loeb, G. J. Muscle Res. Cell Motility 20, 627– 643 (1999).
Taira, M., Boline, J., Smyrnis, N., Georgopoulos, A. & Ashe, J. Exp. Brain. Res. 109, 367– 376 (1996).
Fetz, E. Behav. Brain Sci. 15, 679–690 (1992).
Evarts, E.V. J. Neurophysiol. 31, 14–27 (1968).
Georgopoulos, A. P., Kalaska, J. F., Caminiti, R. & Massey, J. T. J. Neurosci. 2 1527–1537 (1982).
Kuhn, T. S. The Structure of Scientific Revolutions 2nd edn. 150 (University of Chicago Press, Chicago, 1970).
Cisek, P. & Scott, S. H. Neurosci. Lett. 272 , 1–4 (1999).
Scott, S. H. Can. J. Physiol. Pharm. (in press).
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Georgopoulos, A., Ashe, J. One motor cortex, two different views. Nat Neurosci 3, 963 (2000). https://doi.org/10.1038/79882
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DOI: https://doi.org/10.1038/79882
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