MDL – Method Detection Limit
The minimum concentration of an analyte that can be measured and reported within 99% confidence that the concentration of the analyte is greater than zero. The MDL is defined as the (standard deviation) time the (student’s “t” value). The student’s “t” value is determined only by the number of replicates you run; the minimum number of replicates is seven.
|Number of Replicates||Student “t” values for 99%|
LOD – Limit of Detection: The lowest concentration level that can be determined to be statistically different from a blank. The LOQ is usually defined as 3 times the standard deviation. It is approximately equal to the MDL.
LOQ – Limit of Quantification: The concentration above which quantitative results may be obtained with a specific degree of confidence. This is usually defined as 10 times the standard deviation.
Conc/MDL: The (concentration of the standard used to run this test) DIVIDED BY the MDL, (which you will calculate). This must be between 1 and 5. In practice, you should shoot for 3 to 5, because if it ends up being 1, you will be at the MDL, which will cause you a great deal of problems. If it ends up at less than 1, you will have to run the entire test over at a higher concentration.
% Recovery: (Individual result) x 100%/True Value. These should all be between 80% and 120%.
Mean % Recovery: (Mean result) x 100%/True Value. This should be between 80% and 120%.
Signal to Noise Ratio: Mean divided by standard deviation. Should be approximately 2.5 to 10.
Why do I have to do all this stuff?
The first reason is that, with lower and lower effluent limits, there is a need to ensure that the method and technique used in each lab is sufficiently accurate to guarantee that the reported results are meaningful, at least as low as the effluent limit for each analyte. The second reason is that your regulator told you to do so.
Is this hard to do?
Not at all. The actual testing isn’t much more than you do on a daily basis. The only difference is that you will need to run AT LEAST seven replicates. The calculations take a little time, but are not difficult. All you need is a calculator that adds, subtracts, multiplies, divides, squares, and takes square roots. You actually run the test only once, and the rest is mere calculations with the data you recorded for the replicates.
Which analytes do I need to do this for?
According to the information we have, most states DO NOT require these determinations for DO, BOD, TSS, pH, or Fecals. You will probably need to do this determination for all other analytes on your permit. In most cases this means ISE probe methods, spectrophotometric procedures, and titrations. Check with you state regulators to be sure.
A minimum of seven replicates of a standard are required. We recommend that you run nine or ten. It is worth your time, in case of bad data points (outliers), spillage, etc. If you only run seven and one is bad, you will need to run the entire test over, because seven points are required.
“Outliers” are data points that are so far removed from the rest of the points that you are allowed to discard them purely on a mathematical basis. Two acceptable outlier tests are the “Dixon Outlier Test” and “Grubbs Outlier Test”. Consult a statistics reference for these. The explanations and examples are somewhat lengthy, and if we take the time to do this here, we may never get this web page done. Run the tests carefully, and with a little luck, you will not need to test for “outliers”.
– Ammonia Probes: Standardize your probe with standards of 0.1 ppm, 1.0 ppm, and 10.0 ppm. Prepare one liter (1000 ml) of 0.05 ppm. This will give you enough standard to run ten 100 ml samples. Record the results of each individual sample.
– Chlorine Probes: Same as ammonia probes, using chlorine standards and reagents, of course.
– Phosphorus (by spectrophotometer): Prepare at least six standards and a blank. Measure the Absorbance of each standard and use a linear regression to calculate your curve. If necessary, consult “Phosphorus” and “Linear Regression” in the “Technical Tips” section of this website. Prepare one liter of 0.05 ppm standard. Divide into 10 separate samples. Run each sample through the entire procedure. Measure and record the Absorbance of each sample. Using your linear regression equation, calculate the ppm of each standard.
– DPD Chlorine (by spectrophotometer): Same as phosphorus, using chlorine standards and reagents, of course.
Once you get the data points, the calculations are the same for all tests. For brevity, the following example uses only 8 data points. You can use as many as you want, but not less than seven.
First, list the individual results. Then add them up. Then divide by the number of samples. This is the “mean” (average).
|Sample #||Reading (ppm)|
The mean is 0.4071 divided by 8, or 0.0509.
Now, we expand the above table. In the third column, we list the mean, which of course will be the same for each sample. In the fourth column, we subtract each individual result from the mean. In the fifth column, we take the number in the fourth column and square it (multiply each number by itself) and record that result in the fifth column. Note that any negative number squared becomes a positive number. Then add up the numbers in the fifth column.
|Sample #||Reading (ppm)||Mean||Difference from Mean||Difference Squared|
Now divide the total of column five by (n-1) where “n” is the number of samples. In this example, there are eight replicates, so n-1 = 8-1, or 7.
0.0001612 divided by 7 = 0.0000230
Now, using your calculator, take the square root of the number. The square root of 0.0000230 is 0.0047988, or rounding off, 0.0048. THIS IS THE STANDARD DEVIATION!
Now going back to the definitions at the top of this page:
MDL = (standard deviation) times (student’s “t” value for 8 replicates)
MDL = 0.0048 x 2.998 = 0.014 ppm
LOD = 3 times (standard deviation)
LOD = 3 x 0.0048 = 0.014 ppm
LOQ = 10 times (standard deviation)
LOQ = 10 x 0.0048 = 0.048
Conc/MDL = 0.05 ppm/0.014 ppm = 3.57
Is this number between 1 and 5? Yes.
% Recovery (individual) = (individual result) x 100%/True Value
|Sample #||Reading (ppm)||True Value||% Recovery|
Mean % Recovery = (mean) x 100%/True Value
Mean % Recover = 0.0509 x 100%/0.0500 = 101.8%
Signal to Noise Ratio = mean/standard deviation
Signal to Noise Ratio = 0.0509/0.0048 = 10.6
This should be approximately 2.5 to 10.0. The fact that this one is 10.6 is not a problem. It simply means that we could have chosen a standard with a lower concentration to run this test.
The results of this test meet all requirements and therefore could be reported.
These are results of one procedure with our equipment, personnel, standards, and procedure. Feel free to use our calculations as a guide, and our concentrations as a starting point. However, you MUST determine your own MDL’s, LOD’s, LOQ’s, etc., for your lab and your circumstances.