Statistics for Environmental Engineers

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1


3.3322


3.2958


3.3140


0.0006613


-1


1


1


1.1939


1.1314


1.1627


0.0019544


1


1


1


3.4144


3.4372


3.4258


0.0002591

Note: Values shown for the logarithms of the duplicate observations, x = ln(y), and their average and variance.

30.4



28!01 ml / PMA



1.0805-



1.1627/



-3.4258


/



-3.4335



1.0817/


1.0472-



-3.2770



■3.3140 / PMA



N03 level


(b)


FIGURE 30.1 Cube plots for the nitrate measurement data. (a) Duplicate observations at the eight combinations of settings for a 2 factorial design to compare Methods A and B at two levels of nitrate and two levels of PMA preservative. (b) Average of the duplicate log-transformed at the eight experimental conditions.


Factorial designs can be conveniently represented by coding the high and low nitrate levels of each variable as -1 and +1 instead of using the actual values. The design matrix of Table 30.1, expressed in terms of the coded variables and in standard order, is shown in Table 30.2. The natural logarithms of the duplicate observations are listed. Also given are the averages and the variance of each duplicate pair of log-transformed concentrations. The log-transformation is needed to achieve constant variance over the tenfold range in nitrate concentration.


Method A seems to gives lower values than Method B. PMA does not seem to show any effect. We do not want to accept these impressions without careful analysis.

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