Field Sampling for Environmental Science and Management by Webster Richard;Lark Murray;

Author:Webster, Richard;Lark, Murray;
Language: eng
Format: epub
Publisher: Taylor & Francis Group

Under the assumption of a common within-class variance, we obtain the expected mean squared error of prediction from class representatives for the whole region by

(5.21)

in which the subscript p denotes purposive representation. The minimum prediction variance, that is the minimum of MSEp, is again . Here it is reached when the zpk = μk for all k classes.

So, whether we predict z using the means of random samples or from purposively chosen representatives, sets a lower limit to the mean squared error of prediction. In the former case we can approach this minimum by increasing the size of sample; in the latter the observer does it by selecting the representatives to match the mean values as closely as possible.

An observer who wants to improve prediction further using the conventional approach must diminish the within-class variance by refining the classification. This might be done by increasing the scale so that boundaries can be delineated more accurately and intricately, or by subdividing the soil more finely, that is, by increasing the number of classes. In practice the second is likely to demand the first: there is no point in creating classes that cannot be displayed at the chosen scale. Notice that attempting to achieve greater precision in this way requires more work to trace boundaries and a larger sample if there are more classes. It has a cost which is not negligible. Note also that choosing representatives requires experience, and gaining that also has its cost.

In sum, the effectiveness of conventional procedures for soil survey depends both on the quality of the classification and its mapping and on the ability of the surveyor to select representative soil profiles in the field, where the values of the properties of interest approximate the class means. In particular, MSEp should be less than 2, otherwise the selection is worthless, and 2 should be less than + /N, where N is the total size of sample, otherwise classification confers no benefit.

For the whole procedure to be successful we want

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