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Comment on “Statistical procedures for the evaluation of evapotranspiration computing models” by C.P. Jacovides and H. Kontoyiannis, Agricultural Water Management 27 (1995) 365–371
Agricultural Water Management 37 (1998) 93±94
Letter to the Editor
Comment on ``Statistical procedures for the evaluation of evapotranspiration computing models'' by C.P. Jacovides and H. Kontoyiannis, Agricultural Water Management 27 (1995) 365±371 M. Knottersa,*, J.H. Oude Voshaarb a
DLO Winand Staring Centre for Intergrated Land, Soil and Water Research (SC-DLO), P.O. Box 125, 6700 AC Wageningen, The Netherlands b Centre for Biometry Wageningen, CPRO-DLO, P.O. Box 16, 6700 AA Wageningen, The Netherlands
A t-statistic is presented by C.P. Jacovides and H. Kontoyiannis as a measure of evapotranspiration model performance, in conjunction with the mean bias error (MBE ) and the root mean squared error (RMSE ). Unfortunately, the application of the t-statistic as proposed by the authors is based on a misconception. The authors apparently use the tstatistic to test the following hypotheses: H0 H1
no systematic difference between model estimates and observed values (i.e. expectation of MBE equals zero); systematic difference between model estimates and observations.
If H0 is accepted the authors call the model estimates `significant', in contrast to the usual terminology: if H0 is rejected the result is called significant and one concludes that there is a strong evidence against H0. Formulated in the usual terminology, the authors have applied the t-test to prove the H0-hypothesis. This mistake is often made and many textbooks warn for this (for instance Mead et al., 1993). If the residual standard deviation is large the power of the t-test will be low. This is the case for the results of Bowen's model, for which the differences between the predicted and the observed values have a large standard deviation, resulting in a large RMSE and thus in a low t-value. The authors conclude wrongly, based on their application of the t-test, that Bowen's model has a good performance.
* Corresponding author. Tel.: +31 317 474510; e-mail: [email protected] 0378-3774/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved PII S 0 3 7 8 - 3 7 7 4 ( 9 8 ) 0 0 0 3 3 - X
94
M. Knotters, J.H. Oude Voshaar / Agricultural Water Management 37 (1998) 93±94
We conclude that the application of the t-statistic as proposed by Jacovides and Kontoyiannis, is invalid. However, the other two measures, MBE and RMSE, are still perfect measures for model validation. References Mead, R., Curnow, R.N., Hasted, A.M., 1993. Statistical Methods in Agriculture and Experimental Biology. 2nd edn. Chapman and Hall, London.
Letter to the Editor
Comment on ``Statistical procedures for the evaluation of evapotranspiration computing models'' by C.P. Jacovides and H. Kontoyiannis, Agricultural Water Management 27 (1995) 365±371 M. Knottersa,*, J.H. Oude Voshaarb a
DLO Winand Staring Centre for Intergrated Land, Soil and Water Research (SC-DLO), P.O. Box 125, 6700 AC Wageningen, The Netherlands b Centre for Biometry Wageningen, CPRO-DLO, P.O. Box 16, 6700 AA Wageningen, The Netherlands
A t-statistic is presented by C.P. Jacovides and H. Kontoyiannis as a measure of evapotranspiration model performance, in conjunction with the mean bias error (MBE ) and the root mean squared error (RMSE ). Unfortunately, the application of the t-statistic as proposed by the authors is based on a misconception. The authors apparently use the tstatistic to test the following hypotheses: H0 H1
no systematic difference between model estimates and observed values (i.e. expectation of MBE equals zero); systematic difference between model estimates and observations.
If H0 is accepted the authors call the model estimates `significant', in contrast to the usual terminology: if H0 is rejected the result is called significant and one concludes that there is a strong evidence against H0. Formulated in the usual terminology, the authors have applied the t-test to prove the H0-hypothesis. This mistake is often made and many textbooks warn for this (for instance Mead et al., 1993). If the residual standard deviation is large the power of the t-test will be low. This is the case for the results of Bowen's model, for which the differences between the predicted and the observed values have a large standard deviation, resulting in a large RMSE and thus in a low t-value. The authors conclude wrongly, based on their application of the t-test, that Bowen's model has a good performance.
* Corresponding author. Tel.: +31 317 474510; e-mail: [email protected] 0378-3774/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved PII S 0 3 7 8 - 3 7 7 4 ( 9 8 ) 0 0 0 3 3 - X
94
M. Knotters, J.H. Oude Voshaar / Agricultural Water Management 37 (1998) 93±94
We conclude that the application of the t-statistic as proposed by Jacovides and Kontoyiannis, is invalid. However, the other two measures, MBE and RMSE, are still perfect measures for model validation. References Mead, R., Curnow, R.N., Hasted, A.M., 1993. Statistical Methods in Agriculture and Experimental Biology. 2nd edn. Chapman and Hall, London.