Non-Parametric Prediction Limit
Non-Parametric Prediction Limit
See Also:
Non-Parametric Tolerance Limit
Parametric Prediction Limit with Resampling
The Non-Parametric Prediction Limit can be used as an inter-well comparison, where the prediction limit is calculated from samples from background wells, or an intra-well comparison where the prediction limit is calculated from the historical samples from the selected well.
Intra-well or Inter-well comparisons are selected from Select | Comparison, or from the Prediction Limit right-click menu.
Inter-Well Comparison:
Verification Resampling
To support verification resampling, ChemStat allows you to vary the number of samples compared to the prediction limit for each well. The default number of recent sampling dates is specified from Options | Default Options | Comparison or the prediction limit right-click menu. In most cases, a value of 1 is appropriate. However, you can specify different "recent date" values for each individual well. When the prediction interval report is displayed, the bottom portion of the window will display a list of all compliance wells included in the analysis. Select a well or wells. Click the right mouse button to display the context menu, and select the desired number of recent dates for the selected well(s).
Description:
The inter-well non-parametric prediction limit is recommended in the 1992 guidance for data where the assumptions of normality or transformed-normality can not be justified, or when a significant portion of the samples are non-detects. A very basic test, the non-parametric prediction limit simply compares each individual down-gradient concentration for the selected dates, to the maximum concentration in background samples. The prediction limit does not produce an actual limit, but simply a maximum value of the parameter concentration above which contamination is assumed.
The only mathematical calculation is to determine the coverage or level of significance of the test. The level of coverage is dependent on the number of background samples and the selected number of recent dates to compare to the limit.
The inter-well non-parametric prediction limit compares samples from background wells to a selected number of recent sampling dates from compliance wells. If there are more than one sample per date, the samples for that date are averaged. The number of recent sampling dates is specified in the list of wells in the lower pane of the prediction limit menu. In most cases, a value of 1 is appropriate.
Use:
As an inter-well comparison, the non parametric prediction limit is useful for comparison of individual compliance well samples to pooled background data where data do not follow a normal or transformed-normal distribution, and/or there is an abundance of non-detects.
The test is performed on all compliance wells for the specified parameter.
Remarks:
This method will tend to have a high rate of false negatives unless there is a sufficient number of samples available from background wells. The method is not well documented for use on actual data in the 1992 guidance. For this reason, and because of the lack of power of the method, it should be used only when other methods are not available.
Intra-Well Comparison:
Description:
Although not described in the USEPA guidance documents, non-parametric prediction intervals can be used for an intra-well comparison. The Intra-Well Non-Parametric Prediction Limit compares a selected number of recent samples to a specified number of historical baseline samples from the same well.
The only significant calculation is to determine the coverage or level of significance of the test. The level of coverage is dependent on the number of historical samples and the selected number of recent dates.
Use:
As an intra-well comparison, the non parametric prediction limit is useful for assessing potential contamination in a well without the possibility of false positives resulting from natural variability of the ground water quality.
Remarks:
Although easy to implement, as an intra-well comparison, this method requires a large number of historical samples to achieve a reasonable statistical power. To achieve a 95% confidence level, approximately 20 historical samples (known not to be impacted by the facility) are required for each future sample to be compared. It would be unusual to have a facility with this large number of samples, and not be able to apply some other analysis method.
The method is not well documented for use on actual data in the 1992 guidance. For this reason, and because of the lack of power of the method, it should be used only when other methods are not available.