Statistics detection limit

Figs. 2.13-2.15 show representative chromatograms for each of the trace anions at close to the statistical detection limit. The initial injection is shown on a logarithmic scale of conductance to include complete peaks of the major constituents. The recycle portion of the chromatogram was obtained at the linear scale, usually lps cm-1 full scale sensitivity. Fig. 2.14 shows a second collection and recycling of selenite. The process can be repeated indefinitely but there is evidence (below) of 10-15% loss of material each time. 

The ability to demonstrate that two samples have different amounts of analyte is an essential part of many analyses. A method s sensitivity is a measure of its ability to establish that such differences are significant. Sensitivity is often confused with a method s detection limit. The detection limit is the smallest amount of analyte that can be determined with confidence. The detection limit, therefore, is a statistical parameter and is discussed in Chapter 4. 

A method s detection limit is the smallest amount or concentration of analyte that can be detected with statistical confidence. The International Union of Pure and Applied Chemistry (lUPAC) defines the detection limit as the smallest concentration or absolute amount of analyte that has a signal significantly larger than the signal arising from a reagent blank. Mathematically, the analyte s signal at the detection limit, (Sa)dl, is... 

Finally, we have seen that the detection limit is a statistical statement about the smallest amount of analyte that can be detected with confidence. A detection limit is not exact because its value depends on how willing we are to falsely report the analyte s presence or absence in a sample. When reporting a detection limit, you should clearly indicate how you arrived at its value. 

The development of the 3DAP has made it possible to analyse much larger areas of an interface, which improves the statistics as well as the detection limit. Thomson and Miller (2000) provide an impressive example of this technique, as shown in... 

The limit of detection (detection limit, LD), xld, being the lowest content (concentration) which produces a signal y > yc with high statistical probability... 

Helsel DR (1990) Less than obvious statistical treatment of data below the detection limit. Environm Sci Technol 24 1756... 

Statistical evaluation of HPLC UV MS[19] and CE UV MS[20] methods proves that MS detection of anthraquinone dyes is more sensitive than UV, especially in the case of chromatographic analysis of laccaic acids (almost 20 times) and purpurin (almost 40 times). However, detection limits of HPLC ESI MS determination of alizarin and purpurin (0.03 gg ml ) are about 20 times lower than those of CE ESI MS (0.52 0.58 gg ml x). 

Quantification of the limits of detection (LOD), or minimum detectable levels (MDL statistically defined in Section 13.4), is an important part of any analysis. They are used to describe the smallest concentration of each element which can be determined, and will vary from element to element, from matrix to matrix, and from day to day. Any element in a sample which has a value below, or similar to, the limits of detection should be excluded from subsequent interpretation. A generally accepted definition of detection limit is the concentration equal to a signal of twice (95% confidence level) or three times (99% confidence) the standard deviation of the signal produced by the background noise at the position of the peak. In practice, detection limits in ICP-MS are usually based on ten runs of a matrix matched blank and a standard. In this case ... 

The minimum detectable level, or detection limit, is defined as that concentration of a particular element which produces an analytical signal equal to twice the square root of the background above the background. It is a statistically defined term, and is a measure of the lower limit of detection for any element in the analytical process. (This definition corresponds to the 95% confidence interval, which is adequate for most purposes, but higher levels, such as 99% can be defined by using a multiplier of three rather than two.) It will vary from element to element, from machine to machine, and from day to day. It should be calculated explicitly for every element each time an analysis is performed. 

The method detection limit is, in reality, a statistical concept that is applicable only in trace analysis of certain types of substances, such as organic pollutants by gas chromatographic methods. The method detection limit measures the minimum detection limit of the method and involves all analytical steps, including sample extraction, concentration, and determination by an analytical instrument. Unlike the instrument detection limit, the method detection limit is not confined only to the detection limit of the instrument. 

Treatment of a real, imperfect calibration data set revealed the full complexity and breadth of the calibration curve -detection limit problem, ranging from varying statistical weights to an uncertain model and data containing possible blunders to an artificially imposed response threshold. 

The beauty of this completely random approach to the analyte detection limit is the direct applicability of the statistical hypothesis testing formalism. Also, long-term trends in calibration slope or backgrounds have little influence. One important assumption is made that the form of the calibration curve [Equation 2c] is fixed. Also, a subtle change has occurred, the operation is no longer linear, with A in the denominator. Thus, the distribution of x is only asymptotically normal, as the relative standard deviation of becomes smaller. 

Samples with high detection limits (e.g. 10 and 50 ppb Au) have been discarded in the following analysis. Figures 1-3 show contour maps for As, Au and W, and Table 1 lists summary statistics for some elements. 

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