Rejection of outlier

The rejection of outliers is a deeply rooted habit techniques range from the haughty I know the truth attitude, to looks different from what we are used to, somebody must have made a mistake , to attempts at objective proof of having observed an aberration. The first attitude is not only imscientific, but downright fraudulent if unacceptable values are discarded and forgot-... 

Evaluation of the results Evaluation of the results consists of (i) technical scrutiny of the consistency and of the quality of the data the acceptance, on technical (not statistical) grounds, of data to be used to calculate the certified value and its uncertainty, (2) the calculation (using the appropriate statistical techniques) of the certified value and its uncertainty. The approach indudes technical discussion of the results among all cooperators, rejection of outliers, statistical evaluation, and calculation of the certified value and uncertainties. 

Table 6.1 shows the results obtained by Sturgeon et al. [21] for a stored coastal water sample. The mean concentrations and standard deviations of replicates (after rejection of outliers on the basis of a simple c test-function) are given for each method of analysis. Each mean reflects the result of four or more separate determinations by the indicated method [21 ]. 

The rejection of outliers from analytical data is one of the most vexed topics. The only valid reason for rejecting a piece of data is when a discernible cause can... 

It is worth noting that a useful rule of thumb can be applied to the rejection of outliers in data. If more than 20% of the data are rejected as outliers, then one should examine the quality of the collected data and the distribution of the results. 

Statistical evaluation of results (detection and rejection of outliers calculation of the means, standard deviations, confidence intervals, combined expanded uncertainties, etc.)... 

Many of the minor metallic elements have concentrations lying within 20% of the average values for shales. This comparison is illustrated by the data in Table VI, which compares the average concentrations in the underclay and overburden samples, after statistical rejection of outliers by the Dixon method (17), with tabulated values from the literature (18). The most notable exception is manganese, for which the average value in shales is 850 ppm but the observed average in the overburden and underclay was 269 ppm. 

Before statistical parameters were developed, the mean of the results reported by each participant in the water metals and water trace elements studies were plotted on normal probability paper to determine the distribution. Values showing a gross deviation from the normal distribution were then rejected as nonrepresentative because of errors in calculation, dilution, or other indeterminate factors and were not used in subsequent calculations. For the water nutrients study, a somewhat more sophisticated, and more objective, computer-programmed technique was used for rejection of outliers. As verified by plotting of the data on probability paper, however, the results were about the same. 

The 2-test allows the rejection of outliers from data by calculating, Q, defined... 

FIGURE 11.9 Outliers, (a) Dose-response curve fit to all of the data points. The potential outlier value raises the fit maximal asymptote, (b) Iterative least squares algorithm weighting of the data points (Equation 11.25) rejects the outlier and a refit without this point shows a lower-fit maximal asymptote. 

FIGURE 11.22 Control charts and outliers, (a) pEC50 values (ordinates) run as a quality control for a drug screen over the days on which the screen is run (abscissae). Dotted lines are the 95% c.l. and the solid lines the 99.7% c.l. Data points that drift beyond the action lines indicate significant concern over the quality of the data obtained from the screen on those days, (b) The effect of significant outliers on the criteria for rejection. For the data set shown, the inclusion of points A and B lead to a c.l. for 95% confidence that includes point B. Removal of point A causes the 95% limits to fall below points B, causing them to be suspect as well. Thus, the presence of the data to be possibly rejected affects the criteria for rejection of other data. 

Figure 1.24. Rejection of suspected outliers. A series of normally distributed values was generated by the Monte Carlo technique the mean and the standard deviation were calculated the largest normalized absolute deviate (residual) z = xi - /.i is plotted versus n (black...

Since the 1993 court decision against Barr Laboratories, 5 tjjg elimination of outliers has taken on a decidedly legal aspect in the U.S. (any non-U.S. company that wishes to export pharmaceuticals or preciwsor products to the U.S. market must adhere to this decision concerning out-of-specifica-tion results, too) the relevant section states that ... An alternative means to invalidate an individual OOS result... is the (outlier test). The court placed specific restrictions on the use of this test. (1) Firms cannot frequently reject results on this basis, (2) The USP standards govern its use in specific areas, (3) The test cannot be used for chemical testing results. ... A footnote explicitly refers only to a content uniformity test, 5 but it appears that the rule must be similarly interpreted for all other forms of inherently precise physicochemical methods. For a possible interpretation, see Section 4.24. 

A potential outlier should always be examined carefully. First we check if there was a simple mistake during the recording or the early manipulation of the data. If this is not the case, we proceed to a careful examination of the experimental circumstances during the particular experiment. We should be very careful not to discard ("reject") an outlier unless we have strong non-statistical reasons for doing so. In the worst case, we should report both results, one with the outlier and the other without it. 

Check for the presence of outliers. If there are suspect values, check by using a statistical test, either the Grubbs or Dixon tests [9]. Do not reject possible outliers just on the basis of statistics. 

Deviation How much each measurement differs from the mean is an important number and is called the deviation. A deviation is associated with each measurement, and if a given deviation is large compared to others in a series of identical measurements, this may signal a potentially rejectable measurement (outlier) which will be tested by the statistical methods. Mathematically, the deviation is calculated as follows ... 

GRUBBY TEST for rejection of an observation is applied in order to determine if one of the observations should be rejected as being an outlier. The following equation was used for the test ... 

Note The ASTM (American Society for Testing Material) uses a different test for rejection of an outlier, called the reduced central value z,- = (x, — x)/s, which has its own table of critical values. 

Eighteen spectroscopic samples paired with fingerstick reference measurements were collected from an individual over 2 days with a time-randomized protocol. A c alibration model was built by fitting a line through the plot of INU versus reference glucose concentration. The model was then applied to 31 samples collected over the next 14 weeks (7 additional samples from the same individual and 24 from different individuals). After rejecting 11 outliers ( 35%), they obtained a correlation coefficient (r) of 0.8 and a standard deviation of 1.2mM. 

All uncertainty estimates start with that associated with the repeatability of a measured value obtained on the unknown. It is neither required for the sake of quality control, nor could it always be economically justified, to make redundant determinations of each measured value, such as would be needed for complete statistical control. Repeat measurements of a similar kind under the laboratory s typical working conditions may have given satisfactory experience regarding the range of values obtained under normal operational variations of measurement conditions such as time intervals, stability of measurement equipment, laboratory temperature and humidity, small disparities associated with different operators, etc. Repeatability of routine measurements of the same or similar types is established by the use of RMs on which repeat measurements are made periodically and monitored by use of control charts, in order to establish the laboratory s ability to repeat measurements (see sect, entitled The responsible laboratory above). For this purpose, it is particularly important not to reject any outlier, unless cause for its deviation has been unequivocally established as an abnormal blunder. Rejection of other outliers leads a laboratory to assess its capabilities too optimistically. The repeatability in the field of a certified RM value represents the low limit of uncertainty for any similar value measured there. 

The standard deviation is the measure of the dispersion of results obtained in replicate measurements that are normally distributed, i.e., the extent to which such measured values are above or below the mean value for the set. Some sets of measured values are not normally distributed and are not described by a standard deviation. Other sets may be normally distributed on the whole, but have a few outlier values that are much higher or lower relative to the mean than inferred from the standard deviation. Such values may be set aside from calculating mean values by applying a specific rejection criterion (e.g. Chauvenet s) this may permit rejection of values that are twice or more the standard deviation larger or smaller than the mean for 10 values, and thrice or more for 100 values. Any rejection of values must be noted and justified when discussing results. 

An excellent review on outlier treatment is given by Beckman and Cook [42], and by Miller [43]. Some scientists do prefer the use of robust statistics instead of outlier detection and rejection [45]. Whether one prefers the use of statistical tests or chooses to use robust statistics, one should be critical of the dataset. Data points should not be eliminated on the basis of statistical significance only. A cause analysis should be performed before discarding outliers. 

The mean of duplicate determinations is calculated, rejecting obvious outliers. In cases CV > 15 % analysis is repeated. The binding percentage of 125I-insulin is calculated, according to the formula ... 

Inclusion or exclusion of outliers can significantly influence exposure assessments, and harmonized outlier rejection criteria are needed. The suitability of existing approaches (e.g. anything beyond three standard deviations is an outlier) to occupational exposure data sets, as well as the role of field study observations, needs to be considered. 

A problem that arises in many cases is that small raw data samples may contain one or more results which appear to be divergent from the remainder the problem may arise in a calibration experiment or in a set of replicate measurements on a test material. Assuming that the cause of the divergence is not immediately apparent e.g. as a result of a transcription error or instrument failure) it is then necessary to decide whether such an outlier can be rejected entirely from the raw data before data processing e.g. logarithmic transformations) and the usual statistical methods are applied. The treatment of outliers is a major topic in statistics. Three distinct approaches are available. ... 

Creek Bed include Na, Mg, Ca, Sr, and Mn. Figures 5 and 6 illustrate the distribution of Sr and Ca in the Kinneman Creek Bed and adjacent sediments. Although some variation in the concentrations is noted from sample to sample, the criteria for being considered to have an even distribution were that the concentrations were colinear when plotted on probability paper and that none of the points could be rejected as outliers by statistical tests (17). 

---