# Statistics for Environmental Engineers

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Two Sampling Methods. To compare two different sampling methods, we might similarly compare determinations made on ten different specimens using sampling method A with those made on ten specimens using method B with all samples coming from the same batch.

Two Processing Methods. By the same principle, to compare standard and modified methods of processing, we might compare determinations from ten batches from the standard process with determinations from ten batches made by the modified process.

The total deviation y — n of an observation from the process mean is due, in part, to three sources: (1) variation resulting only from the testing method, which has error et and standard deviation at; (2) variation due only to sampling, which has error es and standard deviation as; and (3) variation due only to the process, which has error ep and standard deviation ap.

Figure 25.1 shows the dot plots of the data from the three testing schemes along with the sample statistics from Table 25.1. The estimated variance of 0.50 obtained from making ten tests on one specimen provides an estimate of a1,, the testing variance. The variance Vs = 5.21 obtained from ten specimens each tested once does not estimate a] alone, but rather a2s + a^. This is because each specimen value includes not only the deviation es due to the specimen but also the deviation et due to the test. The variance of es + et is as2+ at2because the variance of a sum is the sum of the variances for independent

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