Statistics for Environmental Engineers

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5


7


2


7


9


6


3


Residual


-9.66


-3.13


-11.08


13.46


-6.47


5.41


-6.47


13.93


1.82


-9.66


New y


54.04


60.37


42.72


69.16


79.03


90.01


78.43


96.73


125.02


106.14


Random No.


7


3


10


4


4


1


7


6


5


9


Residual


-6.47


-9.66


-3.33


-10.62


-10.62


6.33


-6.47


1.82


13.46


13.93


New y


57.23


53.84


50.67


45.08


74.88


90.93


78.43


84.62


136.66


129.73

Comments


Another use of simulation is to test the consequences of violation the assumptions on which a statistical procedure rests. A good example is provided by Box et al. (1978) who used simulation to study how nonnormality and serial correlation affect the performance of the f-test. The effect of nonnormality was not very serious. In a case where 5% of tests should have been significant, 4.3% were significant for


Parameter Estimates for the Original Data and for Five Sets of New Data Generated by Resampling the Residuals in Table 50.1


Data Set


bo


bi


Original


49.14


0.358


Resample 1


56.22


0.306


Resample 2


49.92


0.371


Resample 3


41.06


0.410

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