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**Significance and Use**

5.1 This practice can be used in a single laboratory for trace analysis (that is, where: 1) there are concentrations near the lower limit of the method and 2) the measurements system’s capability to discriminate analyte presence from analyte absence is of interest). In these testing situations, a reliable estimate of the minimum level at which there is confidence that detection of the analyte by the method represents true presence of the analyte in the sample is key. Where within-laboratory detection is important to data use, the WDE procedure should be used to establish the within-laboratory detection capability for each unique application of a method.

5.2 When properly applied, the WDE procedure ensures that the 99 %/95 % WDE has the following properties:

5.2.1 *Routinely Achievable Detection—*The laboratory is able to attain detection performance routinely, using studied measurement systems, without extraordinary effort, and therefore at reasonable cost. This property is needed for a detection limit to be practically useful while scientifically sound. Representative equipment and analysts must be included in the study that generates the data to calculate the WDE.

5.2.2 *Inclusion of Routine Sources of Error—*If appropriate data are used in calculation, the WDE practice will realistically account for sources of variation and bias common to the measurement process and routine for sample analysis. These sources include, but are not limited to: 1) intrinsic instrument noise, 2) some typical amount of carryover error, and 3) differences in analysts, sample preparation, and instruments (including signal-processing methods and software versions).

5.2.3 *Exclusion of Avoidable Sources of Error—*The WDE practice excludes avoidable sources of bias and variation, (that is, those which can reasonably be avoided in routine field measurements). Avoidable sources would include, but are not limited to: 1) inappropriate modifications to the method, the sample, measurement procedure, or measurement equipment, and 2) gross and easily discernible transcription errors (provided there was a way to detect and either correct or eliminate such errors in routine sample testing).

5.2.4 *Low Probability of False Detection—*Consistent with a measured concentration threshold (YC), the WCL is a true concentration that will provide a high probability (estimated at 99 %) of true non-detection (and thus a low estimated probability of false detection (α) equal to 1 %). Thus, when a sample with a real concentration of zero is measured, the probability of not detecting the analyte (that is, the probability that the measured value of the blank will be less than the WCL) would be greater than 99 %. To be most useful, this property must be demonstrated for the particular matrix being used, and not just for reagent-grade water.

5.2.5 *Low Probability of False Non-detection—*Where appropriate data have been used for calculations, the WDE provides a true concentration at which there is a high estimated probability (at least 95 %) of true detection (and thus a low estimated probability of false non-detection (β) equal to 5 % at the WDE), with a simultaneously low estimated probability of false detection. Thus, when a sample with a true concentration at the WDE is measured, the probability of detection would be estimated to be at least 95 %. To be useful, this property must be demonstrated for the particular matrix being used, and not just for reagent-grade water.

5.3 When this practice is utilized by a laboratory to develop these false-positive- and false-negative-control point estimates, from data representative of routine operations, the laboratory may confidently claim these levels of false-positive and false-negative control in the future, so long as the data used remain representative of that future operation. The laboratory may also qualify reported data using the appropriate point estimates (for example YC, YD, WCL, WDE) or censor data below the WCL as a valid basis for these data-reporting practices.

5.4 The WDE practice applies to measurement methods for which calibration error (that is, the error in the calibration of the measurement system) is minor relative to the combined other sources of variability. Some examples of other sources and when they may be dominant are:

5.4.1 Sample preparation (dominant especially when calibration standards do not go through sample-preparation steps).

5.4.2 Differences in analysts where a laboratory has more than one person who may perform each method step.

5.4.3 Instrument differences (measurement equipment), which could take the form of differences in manufacturer, model, hardware, electronics, separation columns, sampling rate, chemical-processing rate, integration time, software algorithms, internal-signal processing and thresholds, effective sample volume, and contamination level.

5.5 Reducing calibration error by use of allowable, though more stringent, calibration procedures (for example, multiple concentrations, replication, tight calibration-acceptance criteria, etc.) and through calibration verification (for example, analysis of a traceable standard from a second, independent source, calibration diagnostics) can reduce the magnitude of the calibration error.

5.6 *Alternative Data-Quality Objectives—*Other values for α, β, confidence, etc. may be chosen as parameters; however, this procedure addresses only those stated here in.

5.7 Collectively, the many sources of variation combine to cause within-laboratory measurements at any true concentration to be normally distributed. The assumption of normality is important for some of the statistics used; data normality should be assessed if there is reason to believe this assumption is not valid.

5.8 If control of false negatives is not a data-quality objective, the WCL determined through this procedure provides a sound criterion for future determination of false-positive control; in such cases, the laboratory may confidently claim that true values above the WCL have a statistically significant difference from like-matrix zero-concentration samples (for example, from the method blank), but nothing more.

5.9 Where as-measured values (for example, not corrected for bias), not true values are of interest, YC and YD may be used as these as-measured levels of the WCL and WDE.

**1. Scope**

1.1 This practice provides a procedure for computing a 99 %/95 % Within-laboratory Detection Estimate (WDE) and the associated critical level/value (WCL). The WDE is the minimum concentration, with false positives and false negative appropriately controlled, such that values above these minimums are reliable detections. The WCL is the point at which only false positives are controlled appropriately. A false positive is the reporting of an analyte as present when the analyte is not actually present; false negatives are reports of analyte absence when the analyte is actually present. This practice is distinguished from the Interlaboratory Detection Estimate (IDE) practice in that the IDE Standard utilizes data from multiple, independent laboratories, while this practice is for use by a single laboratory. The IDE would be utilized where interlaboratory issues are of concern (for example, limits for published methods); this practice (and values derived from it) are applicable where the results from a single laboratory, single operator, single instrument, etc. are involved (for example, in understanding, censoring and reporting data).

1.2 The establishment of a WDE involves determining the concentration below which the precision and bias of an analytical procedure indicates insufficient confidence in false-positive and false-negative control to assert detection of the analyte in the future analysis of an unknown number of samples. Most traditional approaches attempt to determine this detection “limit” by estimating precision at only a single, arbitrary point. The WDE approach is intended to be a more technically rigorous replacement for other approaches for estimating detection limits. The WDE practice addresses a number of critical issues that are ignored in other approaches.

1.2.1 First, rather than making a single-point estimate of precision, the WDE protocol requires an estimate of precision at multiple points in the analytical range, especially in the range of the expected detection limit. These estimates are then used to create an appropriate model of the method’s precision. This approach is a more credible way to determine the point where relative precision has become too large for reliable detection. This process requires more data than has been historically required by single-point approaches or by processes for modeling the relationship between standard deviation and concentration.

1.2.2 Second, unlike most other approaches, the WDE process accounts for analytical bias at the concentrations of interest. The relationship of true concentration to measured concentration (that is, the recovery curve) is established and utilized in converting from as-measured to true concentration.

1.2.3 Third, most traditional approaches to detection limits only address the issue of false positives. Although false negatives may not be of concern in some data uses, there are many uses where understanding and/or control of false negatives is important. Without the false-negative-control information, data reported with just a critical-level value are incompletely described and the qualities of data at these levels incompletely disclosed.

1.2.4 Fourth and last, the WDE standard utilizes a statistical-tolerance interval in calculations, such that future measurements may reasonably be expected to be encompassed by the WDE 90 % of the time. Many older approaches have used the statistical confidence interval, which is not intended to encompass individual future measurements, and has been misunderstood and misapplied. Procedures using the confidence interval cannot provide the stated control when the detection-limit value is applied to future sample results; such application is the primary use of these values.

1.3 To summarize, the WDE is computed to be the lowest true concentration at which there is 90 % confidence that a single (future) measurement (from the studied laboratory) will have a true detection probability of at least 95 % and a true non-detection probability of at least 99 % (when measuring a blank sample). For the laboratory in the study, the critical value is the true concentration at which, on average, (with approximately 90 % confidence) will not be exceeded by 99 % of all measurements of samples with true concentration of zero (that is, blanks). These values are established by modeling the precision and establishing the recovery/bias over a range of concentrations, as well as by using a tolerance interval. The complexities of the WDE procedure may appear daunting, but the additional considerations are necessary if meaningfully estimates of the actual detection capabilities of analytical methods are to be made. The concepts are tractable by degreed chemists, and the use of the available ASTM DQCALC Excel-based software makes the data analysis and limit determinations easy.

1.4 A within-laboratory detection estimate is useful in characterizing the concentration below which a method, for an analyte, as implemented in a specific laboratory, does not (with high confidence) discriminate the presence of the analyte from that of the absence of an analyte. As such an estimator, the WDE Standard (and the WDE and WCL values produced through its application) are useful where a trace-analysis testing method needs to be used.

**2. Referenced Documents** *(purchase separately)* The documents listed below are referenced within the subject standard but are not provided as part of the standard.

**ASTM Standards**

D1129 Terminology Relating to Water

D6091 Practice for 99 %/95 % Interlaboratory Detection Estimate (IDE) for Analytical Methods with Negligible Calibration Error

D7510 Practice for Performing Detection and Quantitation Estimation and Data Assessment Utilizing DQCALC Software, based on ASTM Practices D6091 and D6512 of Committee D19 on Water

E1763 Guide for Interpretation and Use of Results from Interlaboratory Testing of Chemical Analysis Methods

**ICS Code**

ICS Number Code 17.020 (Metrology and measurement in general)

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**DOI:** 10.1520/D7782-13

**Citation Format**

ASTM D7782-13, Standard Practice for Determination of the 99 %/95 % Critical Level (WCL) and a Reliable Detection Estimate (WDE) Based on Within-laboratory Data, ASTM International, West Conshohocken, PA, 2013, www.astm.org

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