Statistical test outlier

Statistical test for deciding if an outlier can be removed from a set of data. 

Dixon s Q-test statistical test for deciding if an outlier can be removed from a set of data. (p. 93) dropping mercury electrode an electrode in which successive drops of Hg form at the end of a capillary tube as a result of gravity, with each drop providing a fresh electrode surface, (p. 509)... 

Outlier detection methods, n - statistical tests which are conducted to determine if the analysis of a spectrum using a multivariate model represents an interpolation of the model. 

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. 

Section 1.6.2 discussed some theoretical distributions which are defined by more or less complicated mathematical formulae they aim at modeling real empirical data distributions or are used in statistical tests. There are some reasons to believe that phenomena observed in nature indeed follow such distributions. The normal distribution is the most widely used distribution in statistics, and it is fully determined by the mean value p. and the standard deviation a. For practical data these two parameters have to be estimated using the data at hand. This section discusses some possibilities to estimate the mean or central value, and the next section mentions different estimators for the standard deviation or spread the described criteria are fisted in Table 1.2. The choice of the estimator depends mainly on the data quality. Do the data really follow the underlying hypothetical distribution Or are there outliers or extreme values that could influence classical estimators and call for robust counterparts ... 

Some statistical tests are specific for evaluation of normality (log-normality, etc., normality of a transformed variable, etc.), while other tests are more broadly applicable. The most popular test of normality appears to be the Shapiro-Wilk test. Specialized tests of normality include outlier tests and tests for nonnormal skewness and nonnormal kurtosis. A chi-square test was formerly the conventional approach, but that approach may now be out of date. 

The organizing laboratory performs statistical tests on the results from participating laboratories, and how outliers are treated depends on the nature of the trial. Grubbs s tests for single and paired outliers are recommended (see chapter 2). In interlaboratory studies outliers are usually identified at the 1% level (rejecting H0 at a = 0.01), and values between 0.01 < a < 0.05 are flagged as stragglers. As with the use of any statistics, all data from interlaboratory studies should be scrutinized before an outlier is declared. 

One can conclude that ANOVA can be a very useful test for evaluating both systematic and random errors in data, and is a useful addition to the basic statistical tests mentioned previously in this chapter. It is important to note, however, there are other factors that can greatly influence the outcome of any statistical test, as any result obtained is directly affected by the quality of the data used. It is therefore important to assess the quality of the input data, to ensure that it is free from errors. One of the most commonly encountered errors is that of outliers. 

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. 

A third source of uncertainty is the occurrence of rare or unique events in the measurement, such as an incorrect reading by the observer, or a chance disturbance in the equipment. Such errors can often produce large deviations from the other readings, and are hence termed outliers . There are statistical tests for recognising such data points, but the occurrence of outliers can be a real problem in statistical data analysis. 

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). 

After outliers have been purged from the data and a model has been evaluated visually and/or by, e.g. residual plots, the model fit should also be tested by appropriate statistical methods [2, 6, 9, 10, 14], The fit of unweighted regression models (homoscedastic data) can be tested by the ANOVA lack-of-fit test [6, 9]. A detailed discussion of alternative statistical tests for both unweighted and weighted calibration models can be found in Ref. [16]. The widespread practice to evaluate a calibration model via its coefficients of correlation or determination is not acceptable from a statistical point of view [9]. 

There is rather significant scattering of data and some of the eight experiments may be regarded as outliers. Therefore we have tested the null hypothesis H0 of equality of the lowest mean of corrosion rate in experiment No 1 and the highest mean in experiment No 8. The calculated value F=s12/s82=5.92/5.02=1.4 for standard deviations was compared with Fisher distribution statistical test values... 

Analysis of the data presented in Table 16.6 allows the rejection of anomalous data (outliers) using statistical tests, producing better precision, from 2.94 to 5.01 (RSDr) and from 7.50 to 13.84 (RSDr). These precision parameters are considered acceptable, and this preliminary validation of the colorimetric method was therefore considered successful. 

Some outliers may also be identified by statistical tests (see Chapter 14), but no single method is capable of detecting outhers in every situation that may occur. The number of techniques suggested or recommended is, for that reason, very large. " The two main problems encountered are as follows ... 

Detection of aberrant (outlier) or suspected values The Grubbs test is the statistical test used to identify if there are some aberrant (outlier) or suspected values, the risk taken is also 5% (Feinberg, 2001). Aberrant or suspected values can also be checked graphically through Box and Whiskers plots. 

Various statistical tests can be performed to determine if a result is an outlier (see Section 7D). 

Several other statistical tests have been developed to provide criteria for rejection or retention of outliers. Such tests, like the Q test, assume that the distribution of the population data is normal, or Gaussian. Unfortunately, this condition cannot be... 

The blind application of statistical tests to retain or reject a suspect measurement in a small set of data is not likely to be much more fruitful than an arbitrary decision. The application of good judgment based on broad experience with an analytical method is usually a sounder approach. In the end, the only valid reason for rejecting a result from a small set of data is the sure knowledge that a mistake was made in the measurement process. Without this knowledge, a cautious approach to rejection of an outlier is wise. 

The search for points called outliers, responsible for a coefficient of variation greater than the fixed value is based on a statistical test (Dixon test). The UV spectra eliminated following this test are considered as not representative of the studied flux. Then, a final statistical test is carried out (Rank test, for example) in order to check if the revealed point is a true isosbestic point. This final test is carried out at X/p 10 nm. 

Grand mean The mean of all the data (used in ANOVA). (Section 4.2) Gross error A result that is so removed from the true value that it cannot be accounted for in terms of measurement uncertainty and known systematic errors. In other words, a blunder. (Section 1.7) Grubbs s test A statistical test to determine whether a datum is an outlier. The G value for a suspected outlier can be calculated using G = ( vsuspect — x /s). If G is greater than the critical G value for a stated probability (G0.05",n) the null hypothesis, that the datum is not... 

Outlier A datum from a sample, assumed to be normally distributed, which lies beyond the mean at a stated probability. Therefore, an outlier is a datum that, according to a statistical test, does not belong to the distribution of the rest of the data. (Section 3.5)... 

In cases where a failing calibration standard or QC result is deemed an outlier based on a statistical test, the actual result should be reported. Precision and accuracy calculations can be presented both with and without the outlier results to facilitate an assessment of the overall impact of the anomalous value. When anomalous results are numerous, the bioanalytical investigator should determine if the results are indicative of a pervasive method problem. 

Statistical tests make possible the automatic detection of an outlier in both cases (they are defined as outliers in the first case and Q outliers in the second case). With these simple tests it will be possible to detect a fault in a process or to reject a bad product by checking just two plots, instead of as many plots as variables as in the case of the Sheward charts commonly used when the univariate approach is applied. Furthermore, the multivariate approach is much more robust, since it will lead to a lower number of false negatives and false positives, and much more sensitive, since it allows the detection of faults at an earlier stage. Finally, the contribution plots will easily outline which variables are responsible for the sample being an outlier. 

Each of these procedures has its own advantages and disadvantages, but each, if properly applied, is capable of leading to reliable certification. The methods used at IAEA (Parr, 1984, Parr et al. 1988) involve a dual approach. On the one hand, statistical tests are applied to eliminate outliers in addition, however, various acceptance criteria are applied of which the most important are (1) that data should be available from at least two different analytical methods for the calculation of the consensus value, and (2) that there should be no significant differences between the groups of accepted results obtained by different analytical methods. 

There are a variety of statistical tests that have been used to decide if a data point should be rejected, as well as some rules of thumb . The range chosen to guide the decision will limit all of these tests and guidelines. A large range will retain possibly erroneous results, while a very small range will reject valid data points. It is important to note that the outlier must be either the highest value in the set of data or the lowest value in the set. A value in the middle of a data set cannot be discarded unless the analyst knows that an error was made. 

The test statistics at all concentrations exceed the critical values at 5%, but not at 1%. By ISO 5725-2 definition, this classifies them as stragglers, but not as outliers. Application of Grubb s outlier test [Eqs. (9.26) and (9.27)] to the data submitted by laboratory 5 (Table 9.14, where G represents Grubb s outlier statistic) suggests that there are no statistically significant outliers. 

Before using QC data, an appropriate statistical test, such as Grubb s or Dixon s tests, should be applied to test for outliers. Those data points acquired during a period in which the method was not in statistical control should not be included in the calculations. This approach assumes that measurements are being made at concentrations where the relative uncertainty is constant over a defined range, the constant uncertainty that would dominate at concentrations close to the limit of detection or limit of quantification is negligible, and that recovery is independent of concentration. 

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