Statistics for Environmental Engineers

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14


Winkler


1.2


1.4


1.4


1.3


1.2


1.3


1.4


2.0


1.9


1.1


1.8


1.0


1.1


1.4


Electrode


1.6


1.4


1.9


2.3


1.7


1.3


2.2


1.4


1.3


1.7


1.9


1.8


1.8


1.8


Diff. (W — E)


-0.4


0.0


0.5


1.0


-0.5


0.0


0.8


0.6


0.6


0.6


0.1


0.8


-0.7


-0.4

Source: Wilcock, R. J., C. D. Stevenson, and C. A. Roberts (1981). Water Res., 15, 321-325.


1    5    10    14


Laboratory


FIGURE 17.1 The DO data and the differences of the paired values.

Theory: The Paired f-Test Analysis


Define S as the true mean of differences between random variables yj and y2 that were observed as matched pairs under identical experimental conditions. S will be zero if the means of the populations from which yj and y2 are drawn are equal. The estimate of S is the average of differences between paired observations:




Because of measurement error, the value of d is not likely to be zero, although it will tend toward zero if S is zero.


The sample variance of the differences is:


E(d.-df


П — 1


The standard error of the average difference d is:

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