Statistics for Environmental Engineers

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The method is demonstrated using the 45 values in Table 15.3 (these are random normal values). The concentrations have been ranked and the rankits are from the tables of Rohlf and Sokal (1981). Figure 15.3 shows the probability plots. The top panel shows the 45 normally distributed observations. The linear regression of concentration on rankits estimates a mean of 33.3 and a standard deviation of 5.4. The middle panel shows the result when the 10 smallest observations are censored (22% censoring). The bottom panel has the lowest 20 values censored (44% censoring) so the mean can still be estimated without extrapolation. The censoring hardly changed the estimates of the mean and standard deviation. All three data sets estimate a mean of about 33.5 and a standard deviation of about 5. It is apparent, however, that increased censoring gives more relative weight to values in the upper tail of the distribution.


Censored Data Analysis Using Rankits (Normal Order Statistics)


Conc.


Rankit


Conc.


Rankit


Conc.


Rankit


23.8


2.21


31.0


-0.40


36.4


0.46


24.4


-1.81


31.6


-0.34


37.0


0.52


25.0


-1.58


31.6


-0.28


37.0


0.59


25.0


-1.41


31.6


0.22


37.0


0.65


25.6


1.27


32.2


0.17


37.0


0.72


25.6


-1.16


32.8


0.11


37.0


0.80


28.0


-1.05


33.4


-0.06


37.6


0.88

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