Statistics for Environmental Engineers

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This example shows how errors that seem large do not always propagate into large errors in calculated values. But the reverse is also true. Our intuition is not very reliable for nonlinear functions, and it is useless when several equations are used. Whether the error is magnified or suppressed in the calculation depends on the function and on the level of the variables. That is, the final error is not solely a function of the measurement error.

Random and Systematic Errors

The titration example oversimplifies the accumulation of random errors in titrations. It is worth a more complete examination in order to clarify what is meant by multiple sources of variation and additive errors. Making a volumetric titration, as one does to measure alkalinity, involves a number of steps:

1.    Making up a standard solution of one of the reactants. This involves (a) weighing some solid material, (b) transferring the solid material to a standard volumetric flask, (c) weighing the bottle again to obtain by subtraction the weight of solid transferred, and (d) filling the flask up to the mark with reagent-grade water.

2.    Transferring an aliquot of the standard material to a titration flask with the aid of a pipette. This involves (a) filling the pipette to the appropriate mark, and (b) draining it in a specified manner into the flask.

3. Titrating the liquid in the flask with a solution of the other reactant, added from a burette. This involves filling the burette and allowing the liquid in it to drain until the meniscus is at a constant level, adding a few drops of indicator solution to the titration flask, reading the burette volume, adding liquid to the titration flask from the burette a little at a time until the end point is adjudged to have been reached, and measuring the final level of liquid in the burette.

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