# Detection & Quantitation

EPA received many questions about hazardous waste test methods. The questions and responses for this category are listed below.

**On this page:**

- Is the use of weighted least squares regression appropriate for solid and hazardous waste measurements of cyanide and phenol instead of linear regression?
- Use of 2-tailed vs. 1-tailed t-values in SW-846 Chapter 9 formula for calculating confidence limits.
- How should the lower limit of quantitation (LLOQ) for total Xylenes be reported for SW-846 test methods?
- What is meant by the Lower Limit Of Quantitation (LLOQ) for SW-846 test methods?
- Are Method Detection Limit (MDL) studies required for SW-846 test methods?

## Is the use of weighted least squares regression appropriate for solid and hazardous waste measurements of cyanide and phenol instead of linear regression?

Is the use of weighted least squares regression appropriate for solid and hazardous waste measurements of cyanide and phenol instead of linear regression, specifically as it relates to EPA 9012B and EPA 9066 sample analyses?

Ordinary least squares (OLS) regression is a specific application of weighted least squares (WLS) regression in which each of the weighting factors is assigned a value of unity (“1”). OLS is straightforward – especially when applied to a linear model – and the rationale for use and underlying mathematics are easily understood. However, implicit in OLS is the assumption that the variance associated with each calibration level is constant across the entire calibration range. Intuitively, we know that this assumption is not entirely valid. As a result, un-weighted OLS regression tends to generate calibration curves that fit higher concentration points more closely than those at lower concentrations.

Weighted least squares (WLS) regression would appear to be an attractive alternative and in principle WLS regression yields more representative fitting of experimental data when properly applied to a sufficient number of data points. However, estimation of appropriate weighting factors is challenging, and poor estimates may significantly impact the quality of the fitted data to the empirical calibration model.

For example, in the ideal case, WLS requires that replicate calibration standards be analyzed at each concentration level in order to assess variance for each concentration value. Clearly, this is not a practical approach for the production laboratory. SW-846 Method 8000 discusses approaches to calibration for gas chromatography methods, and provides example weighting factors that are reciprocal values of either concentrations, concentrations squared, or of variances themselves (if available). Each approach has its advantages as well as limitations.

WLS may be an appropriate calibration modeling approach for cyanides and phenol if supported by the empirical data, characteristics of the methods, and other program-specific needs. Any model applied to actual data should do more than just “fit the data” – it should be supported by the analytical methodology, detection characteristics, and physiochemical behavior of the analyte within the measurement system. For example, in optical absorption spectroscopy, we have a well-defined physical model that relates the linear relationship between analyte concentrations to absorption of incident radiation called the Beer-Lambert Law. If we happened to measure calibration sample responses and found that a quadratic model yielded an acceptable representation of those data, use of this model would be in direct contrast to what we know about absorption of light and would not be valid (even though it “worked”).

A summary overview of various EPA programs’ uses and needs for calibration curve modeling can be found in "Calibration Curves: Program Use/Needs".

Other Category: 9000 Series

## Use of 2-tailed vs. 1-tailed t-values in SW-846 Chapter 9 formula for calculating confidence limits.

The Chapter 9 formula for calculating confidence limit appears to use the 2‐tailed t‐value to evaluate sample data against a regulatory limit at 80% confidence. However, this type of evaluation involves a one‐sided hypothesis (sample mean > regulatory limit) and requires a 1‐tailed t‐value which is a much smaller value than indicated in the Chapter 9 t‐value table.

Is this a mistake in the text or is there some reason for using the 2‐tailed t‐value when a 1‐tailed t‐value is typically used?

There is no mistake in the Chapter 9 text regarding use of the 2-tailed t-value. Using a 0.2 probability (80% confidence interval) with the 2-tailed t-value and only looking at the upper end to determine if it exceeds the hazardous waste level, is in effect, using a 1-tailed t-value at 0.1 probability (90% confidence interval). The equivalency is mentioned in the parentheses in footnote b under Table 9.2: "Tabulated "t" values are for a two-tailed confidence interval and a probability of 0.20 (the same values are applicable to a one-tailed confidence interval and a probability of 0.10)."

Calculation wise, use Equation 6 where the confidence interval is expressed as the mean plus or minus the 0.2 t-statistic times the standard deviation. For hazardous waste determination, we are only using the mean plus the 0.2 t-statistic times the standard deviation and ignoring the mean minus the 0.2 t-statistic times the standard deviation.

Finally, Section 9.1.1.1 states, "For the purposes of evaluating solid wastes, the probability level (confidence interval) of 80% has been selected. That is, for each chemical contaminant of concern, a confidence interval (CI) is described within which μ occurs if the sample is representative, which is expected of about 80 out of 100 samples. The upper limit of the 80% CI is then compared with the appropriate regulatory threshold. If the upper limit is less than the threshold, the chemical contaminant is not considered to be present in the waste at a hazardous level; otherwise, the opposite conclusion is drawn. One last point merits explanation. Even if the upper limit of an estimated 80% CI is only slightly less than the regulatory threshold (the worst case of chemical contamination that would be judged acceptable), there is only a 10% (not 20%) chance that the threshold is equaled or exceeded. That is because values of a normally distributed contaminant that are outside the limits of an 80% CI are equally distributed between the left (lower) and right (upper) tails of the normal curve. Consequently, the CI employed to evaluate solid wastes is, for all practical purposes, a 90% interval." In other words, the 80% two-tailed value effectively becomes a 90% one-tailed value when we only consider the upper end.

## How should the lower limit of quantitation (LLOQ) for total Xylenes be reported for SW-846 test methods?

How should the LLOQ for total Xylenes be reported, i.e., a sum of the LLOQ for the 3 isomers?

Unless a separate integration for total xylenes is performed, the xylene isomer LLOQs should be added together. Similarly, when reporting total xylenes, the results of m&p xylene and o-xylene should be added together.

It is important to point out that m- and p-xylene are difficult to chromatographically separate under the conditions described in methods 8015 and 8260, while separation of the o-xylene peak from m+p-xylenes is easier to achieve. If both m- and p-xylenes are present in a mixed stock solution at the same concentration, then the calibration range for the peak representing m- and p-xylene would be twice as high as for other target analytes. Along with their corresponding lower limit of quantitation (based on the low standard concentration).

Other category: 8000 Series

## What is meant by the Lower Limit Of Quantitation (LLOQ) for SW-846 test methods?

What is LLOQ?

SW-846 Chapter One defines the Lower Limit Of Quantitation (LLOQ) as: The lowest point of quantitation which, in most cases, is the lowest concentration in the calibration curve. The LLOQ is initially verified by spiking a clean control material (e.g., reagent water, method blanks, Ottawa sand, diatomaceous earth, etc.) at the LLOQ and processing through all preparation and determinative steps of the method. Laboratory-specific LLOQ recovery limits should be established when sufficient data points exist. See Section 9 of Methods 8000D and 6010D/6020B for additional guidance in establishing, implementing and verifying LLOQs for organic and inorganic analytes. LLOQs should be determined at a frequency established by the method, laboratory’s quality system, or project.

Other category: QA/QC

## Are Method Detection Limit (MDL) studies required for SW-846 test methods?

Method Detection Limit is no longer defined in Chapter One, nor is it referenced in the SW-846 methods. Does that mean that MDL studies are no longer required?

The EPA Office of Resource Conservation and Recovery (ORCR) that publishes the SW‐846 test methods manual no longer uses the MDL, and promotes the use of the Lower Limit of Quantitation (LLOQ) approach for establishing the reporting limit for a respective test method or laboratory SOP. EPA ORCR is in the process of transitioning existing SW‐846 methods and preparing new methods to specifically address the LLOQ approach and procedures for establishing, implementing, and verifying it.

Other EPA programs (e.g., the Clean Water Act (CWA)) and projects still utilize the MDL concept. In those cases when an MDL is needed, method users may follow the procedure stipulated in Appendix B to 40 CFR Part 136 for determining an MDL.

Other Category: QA/QC