Blank statistics

Fig. 2-4. Blank statistics and confidence band statistics in calibration (according to [MULLER et al., 1994])...

In principle, all performance measures of an analytical procedure mentioned in the title of this section can be derived from a certain critical signal value, ycrit. These performance measures are of special interest in trace analysis. The approaches to estimation of these measures may be subdivided into methods of blank statistics , which use only blank measurement statistics, and methods of calibration statistics , which in addition take into account calibration confidence band statistics. 

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... 

The most useful methods for quality assessment are those that are coordinated by the laboratory and that provide the analyst with immediate feedback about the system s state of statistical control. Internal methods of quality assessment included in this section are the analysis of duplicate samples, the analysis of blanks, the analysis of standard samples, and spike recoveries. 

In a performance-based approach to quality assurance, a laboratory is free to use its experience to determine the best way to gather and monitor quality assessment data. The quality assessment methods remain the same (duplicate samples, blanks, standards, and spike recoveries) since they provide the necessary information about precision and bias. What the laboratory can control, however, is the frequency with which quality assessment samples are analyzed, and the conditions indicating when an analytical system is no longer in a state of statistical control. Furthermore, a performance-based approach to quality assessment allows a laboratory to determine if an analytical system is in danger of drifting out of statistical control. Corrective measures are then taken before further problems develop. 

Using Control Charts for Quality Assurance Control charts play an important role in a performance-based program of quality assurance because they provide an easily interpreted picture of the statistical state of an analytical system. Quality assessment samples such as blanks, standards, and spike recoveries can be monitored with property control charts. A precision control chart can be used to monitor duplicate samples. 

If fondly recall the first day of an introductory graduate statistical mechanics class. As our instructor walked into the class saying something entirely appropriate like So, are we all ready for a lesson in quantum field theory today , he was of course met with a room-full of blank stares (even a few - later embarrassed - behind-the-back giggles). As first-year graduate students we had unfortunately not yet developed the requisite maturity to appreciate the profound link that exists between statistical mechanics and modern field theory. I resolved to never again be as quick to dismiss any obvious disparity or seeming disconnectedness between two subjects. 

Accuracy is the term used to describe the degree of deviation (bias) between the (often unknown) true value and what is found by means of a given analytical method. Accuracy cannot be determined by statistical means the test protocol must be devised to include the necessary comparisons (blanks, other methods). 

Several terms have been used to define LOD and LOQ. Before we proceed to develop a uniform definition, it would be useful to define each of these terms. The most commonly used terms are limit of detection (LOD) and limit of quantification (LOQ). The 1975 International Union of Pure and Applied Chemistry (lUPAC) definition for LQD can be stated as, A number expressed in units of concentration (or amount) that describes the lowest concentration level (or amount) of the element that an analyst can determine to be statistically different from an analytical blank 1 This term, although appearing to be straightforward, is overly simplified. If leaves several questions unanswered, such as, what does the term statistically different mean, and what factors has the analyst considered in defining the blank Leaving these to the analyst s discretion may result in values varying between analysts to such an extent that the numbers would be meaningless for comparison purposes. 

Net recoveries of cyfluthrin from matrices fortified at 0.01-5.05 mg kg ranged from 77 to 119%. The limit of detection (LOD) is defined as the lowest concentration that can be determined to be statistically different from a blank or control. Calculate the value by taking the standard deviation of the residue values from the analysis of the recovery samples at the limit of quantification (LOQ) and using the equation... 

As a rule, the average blank is estimated from repetition measurements of a - not too small - number of blank samples as arithmetic mean yBL. If there is information that another than normal distribution applies, then the mean of this other distribution should be estimated (see textbook of applied statistics see Arnold [1990] Davies and Goldsmith [1984] Graf et al. [1987] Huber [1981] Sachs [1992]). 

The relation of measured results to given values, e.g., critical levels, legally fixed values, regulatory limits, maximum acceptable values, is of continual relevance in analytical chemistry. In the analytical reality, the problematic nature of detection leads to the test statistics, strictly speaking to the t-test (Currie [1995, 1997] Ehrlich and Danzer [2006]). By means of that, it is tested, if the determined analytical result is significantly different from the average blank of the critical value, respectively. 

The limit of detection (LoD) has already been mentioned in Section 4.3.1. This is the minimum concentration of analyte that can be detected with statistical confidence, based on the concept of an adequately low risk of failure to detect a determinand. Only one value is indicated in Figure 4.9 but there are many ways of estimating the value of the LoD and the choice depends on how well the level needs to be defined. It is determined by repeat analysis of a blank test portion or a test portion containing a very small amount of analyte. A measured signal of three times the standard deviation of the blank signal (3sbi) is unlikely to happen by chance and is commonly taken as an approximate estimation of the LoD. This approach is usually adequate if all of the analytical results are well above this value. The value of Sbi used should be the standard deviation of the results obtained from a large number of batches of blank or low-level spike solutions. In addition, the approximation only applies to results that are normally distributed and are quoted with a level of confidence of 95%. 

One common characteristic of many advanced scientific techniques, as indicated in Table 2, is that they are applied at the measurement frontier, where the net signal (S) is comparable to the residual background or blank (B) effect. The problem is compounded because (a) one or a few measurements are generally relied upon to estimate the blank—especially when samples are costly or difficult to obtain, and (b) the uncertainty associated with the observed blank is assumed normal and random and calculated either from counting statistics or replication with just a few degrees of freedom. (The disastrous consequences which may follow such naive faith in the stability of the blank are nowhere better illustrated than in trace chemical analysis, where S B is often the rule [10].) For radioactivity (or mass spectrometric) counting techniques it can be shown that the smallest detectable non-Poisson random error component is approximately 6, where ... 

After you ve taken the multiple-choice practice exam under timed conditions, count the number of questions you got correct. From this number, subtract the number of wrong answers x A Do not count items left blank as wrong. Then refer to this table to find your probable overall AP score. For example, if you get 39 questions correct, based on historical statistics you have a 25% chance of receiving an overall score of 3, a 63% chance of receiving an overall score of 4, and a 12% chance of receiving an overall score of 5. Note that your actual results may be different from the score this table predicts. Also, remember that the free-response section represents 55% of your AP score. 

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 ... 

Data verification, also called quality control (QC), to verify the results before reporting, including statistical analysis of duplicates, standards, and blanks. 

Here the concept of statistical control is not applicable. It is assumed, however, that the materials in the run are of a single type. Carry out duplicate analysis on all of the test materials. Carry out spiking or recovery tests or use a formulated control material, with an appropriate number of insertions (see above), and with different concentrations of analyte if appropriate. Carry out blank determinations. As no control limits are available, compare the bias and precision with fitness-for-purpose limits or other established criteria. 

The olfactometer supplies 6 dilution levels. At each dilution level 3 samples ( triangle ) are presented to the panelist from a set of glass sniffing ports, two presenting the test room air (blanks). The third is the odorous gas sample diluted with test room air. The panelist is instructed that one of the three ports at each dilution level exhibits an odour, and that his task is to smell the effluents from the ports and decide which port, in his opinion, delivers an odorous sample. If the panelist can smell no difference he has to guess ( forced triangle ). This is included in the statistical basis for calculation of the total odour strength. 

From the distribntion of signals of blank measnrements we can derive the critical value. This valne is defined by the one-tailed error probability a of the statistical distribntion. If the signal is above this critical value we have a low probability (a) for a false positive error. 

This low probability is shown in the left of the two distribntions in this graph, the statistical distribntion of blank measurements. At a signal corresponding to the critical value we have the low probability for a false positive error, described by the black part of the distribution. 

---