Statistics for Environmental Engineers

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-0.165


10


49978


60585


-10607


10.819


11.012


-0.192


11


39186


47455


-8269


10.576


10.768


-0.191


12


41074


43584


-2510


10.623


10.682


-0.059


13


8424


6640


1784


9.039


8.801


0.238


14


8995


8244


751


9.104


9.017


0.087


15


8436


8204


232


9.040


9.012


0.028


16


9195


9579


-384


9.126


9.167


-0.041


17


8729


8547


182


9.074


9.053


0.021


Average


33135


36196


-3062


10.164


10.215


-0.051


Std. deviation


20476


23013


4059


0.785


0.861


0.119


Std. error


4967


5582


984


0.190


0.209


0.029

Comments


The paired t-test examines the average of the differences between paired observations. This is not equivalent to comparing the difference of the average of two samples that are not paired. Pairing blocks out the variation due to uncontrolled or unknown experimental factors. As a result, the paired experimental design should be able to detect a smaller difference than an unpaired design. We do not have free choice of which t-test to use for a particular set of data. The appropriate test is determined by the experimental design.


We never really believe the null hypothesis. It is too much to expect that the difference between any two methods is truly zero. Tukey (1991) states this bluntly:

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