Statistics for Environmental Engineers

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n


p


= 2


p


= 3


p


= 4


dL


du


dL


du


dL


du


15


1.08


1.36


0.95


1.54


0.82


1.75


20


1.20


1.41


1.10


1.54


1.00


1.68


25


1.29


1.45


1.21


1.55


1.12


1.66


30


1.35


1.49


1.28


1.57


1.21


1.65


50


1.50


1.59


1.46


1.63


1.42


1.67

Note: n = number of observations;p = number of parameters estimated in the model.


Source: Durbin, J. and G. S. Watson (1951). Biometrika, 38, 159-178.

A Statistic to Indicate Possible Autocorrelation


Detecting autocorrelation in a small sample is difficult; sometimes it is not possible. In view of this, it is better to design and conduct experiments to exclude autocorrelated errors. Randomization is our main weapon against autocorrelation in designed experiments. Still, because there is a possibility of autocorrelation in the errors, most computer programs that do regression also compute the Durbin-Watson statistic, which is based on an examination of the residual errors for autocorrelation. The Durbin-Watson test assumes a first-order model of autocorrelation. Higher-order autocorrelation structure is possible, but less likely than first-order, and verifying higher-order correlation would be more difficult. Even detecting the first-order effect is difficult when the number of observations is small and the Durbin-Watson statistic cannot always detect correlation when it exists.

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