Talk:Nash–Sutcliffe model efficiency coefficient

NSE and R² really the same?!

How can NSE and R² be the same? Why inventing a "new" coefficient to test modells, when theres already one with the same formula?! Or arent they the same?! Confused--132.230.20.106 (talk) 09:55, 7 March 2011 (UTC)

Invent? The exact thing denoted by R² has different definitions or specifications depending on background and approach. NSE and R² are different if R² is interpreted as the square of the correlation coefficient between observed and predicted, and tthis is often the definition used in the context of linear regression. But they are the same if R² is interpreted using the more general formulation outlined in coefficient of determination. At the time of development of NSE, those authors were working in a context where R² was used for the square of the correlation coefficient. "Nash-Suttcliffe" is used as the name for the coefficient in a fairly widespread way in the field in which they were working, which was hydrology and water resources. Melcombe (talk) 10:46, 7 March 2011 (UTC)

Thanks that helped a lot!--Rockwurm (talk) 14:32, 7 March 2011 (UTC)

I think this point needs clarification in both the coefficient of determination and Nash–Sutcliffe model efficiency coefficient articles. Benhenley (talk) 05:38, 20 July 2012 (UTC)

   NSE =                1                - sum((y-yhat)^2)/sum((y-ybar)^2)
       = sum((y-ybar)^2)/sum((y-ybar)^2) - sum((y-yhat)^2)/sum((y-ybar)^2)
       =              (sum((y-ybar)^2) - sum((y-yhat)^2)))/sum((y-ybar)^2)

   R² = sum((y-ybar)^2) / (sum((y-ybar)^2) + sum((y-yhat)^2))

So - theyre different, right? 163.7.134.35 (talk) 04:25, 20 June 2016 (UTC)