Tests for outliers

Ga,n Significance limits of Grubb s outlier test for a risk of error a and n individual measurements ... 

Based on the survey of industry OOS practices mentioned earlier, many laboratories have begun using outlier testing for OOS results from chemical assays, but the test is being used cautiously and only to support solid analytical evidence that confirms the OOS was truly unrepresentative of the sample. It has been used only to augment evidence that an OOS result is invalid since it sheds no technical light on the possible cause of the aberrant result. 

There are two methods commonly used for testing the homogeneity the Cochran and the Bartlett tests. The first is an outlier test for variances and the second tests more for the scattering of variances. In the laboratory of the authors the Bartlett criterium (Pearson and Hartley, 1962) is preferred. 

Standard ISO 5725-2 recommends that suitable procedures be used to detect and remove outliers in data. The procedures used within the ISO 5725-2 document include Mandel s h and k statistics for overall assessment and comparison of between-laboratory and within-laboratory consistency, respectively Cochran s test for evaluating within-laboratory consistency and Grubb s outlier tests for evaluating data. These procedures will also be used for this example. See Equations (9.23)-(9.45) for relevant definitions and equations. MandeTs h and k statistics, given in Tables 9.11 and 9.12, respectively, were calculated using Equations (9.23) and (9.24). 

Outlier tests for cell means as well as for laboratory 5 observations are statistically insignificant. However, the fact that Mandel s k statistics for laboratory 5 were inconsistent with the findings from the other laboratories, and that the Cochran test statistics for all concentrations in laboratory 5 were statistically significant at the 5% but not at the 1% critical value, raises the question as to whether there is a problem with the results reported by laboratory 5. Although... 

The Court s opinion on outliers was that since, for chemical testing, the USP does not provide for outliers, the use of outlier testing for chemical analyses is prohibited. The Court also agreed that the USP specifically allows outlier testing for biological and antibiotic assays. (This opinion has been challenged a number of times on scientific grounds.)... 

An important application of statistical tests is the recognition of outliers. Here, we only consider outliers in a series of measurements. Outlier tests for methods of pattern recognition and modeling are introduced in Chapters 5 and 6, respectively. 

On occasion, a data set appears to be skewed by the presence of one or more data points that are not consistent with the remaining data points. Such values are called outliers. The most commonly used significance test for identifying outliers is Dixon s Q-test. The null hypothesis is that the apparent outlier is taken from the same population as the remaining data. The alternative hypothesis is that the outlier comes from a different population, and, therefore, should be excluded from consideration. 

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

The absorbance of solutions of food dyes is used to explore the treatment of outliers and the application of the f-test for comparing means. 

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)... 

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 test for outliers can be based on this concept, for instance by using... 

Note on GMPs The assays are conducted on individual dosage units (here tablets) and not on composite samples. The CU test serves to limit the variability from one dosage unit to the next (the Dissolution Rate test is the other test that is commonly used). Under this premise, outlier tests would be scientific nonsense, because precisely these outliers contain information on the width of the distribution that one is looking for. The U.S. vs. Barr Laboratories Decision makes it illegal to apply outlier tests in connection with CU and DR tests. This does not mean that the distribution and seemingly or truly atypical results should not be carefully investigated in order to improve the production process. 

Example 53 If the standard deviation before elimination of the purported outlier is not much higher than the upper CLf method), as in the case = 0.358 < CL(/(0.3) 0.57 factor Chu/sx 1.9 for = 9, see program MSD), an outlier test should not even be considered both for avoiding fruitless discussions and reducing the risk of chance decisions, the hurdle should be set even higher, say at p < 0.01, so that CLu/sx > 2.5. 

The FDA did not include outlier tests in the USP for chemical assays, but allowed the practice for biological tests. The reason for this could be that because of the high precision, n is usually small in chemical testing with n < 3, outlier tests cannot be conducted. It appears that Judge Wolin followed this recommendation when deliberating his decision. 

Since the U.S. vs. Barr decision in 1993 (relevant to pharmaceuticals and related fields, rules applied by the Federal Food Drug Administration, FDA), outlier tests may no longer be applied to physicochemical tests, under the assumption that such test methods, having been optimized and validated for the particular set of circumstances, rarely produce outliers. These tests may not be applied to CU results at all. Good manufacturing practices mandate that operators work according to pre-set procedures and write down any observed irregularities as they... 

Other authors used a simple 2 standard deviation criteria or an outlier test (F-test) to check for significant differences between within-bottle and between-bottle results (Martin-Esteban et al. 1997 Quevauviller et al. 1995). The degree of homogeneity of elements and compounds in the materials tested in these studies does not seem to be adequately described and, hence, the asigned uncertainties in the mean values may represent only the bias between the analytical methods used in the certification. 

Among numerous tests for outliers presented in the literature, in analytical practice the following have turned out to be especially useful ... 

In the simplest case, if all sample sub groups have the same size, zzi = n2 =. .. = zzjt, Dixon s test for outliers can be used (see Sect. 4.3.2). Then, in Eq. (4.35), instead of the individual values, the means are entered. 

The above two objectives, data examination and preparation, are the primary focus of this section. For data examination, two major techniques are presented the scattergram and Bartlett s test. Likewise, for data preparation (with the issues of rounding and outliers having been addressed in a previous chapter) two techniques are presented randomization (including a test for randomness in a sample of data) and transformation. Exploratory data analysis (EDA) is presented and briefly reviewed later. This is a broad collection of techniques and approaches to probe data, that is, to both examine and to perform some initial, flexible analysis of the data. 

It is important to appreciate that the statistical significance of the results is wholly dependent on the quality of the data obtained from the trial. Data that contain obvious gross errors should be removed prior to statistical analysis. It is essential that participants inform the trial co-ordinator of any gross error that they know has occurred during the analysis and also if any deviation from the method as written has taken place. The statistical parameters calculated and the outlier tests performed are those used in the internationally agreed Protocol for the Design, Conduct and Interpretation of Collaborative Studies.14... 

Both assumptions are mainly needed for constructing confidence intervals and tests for the regression parameters, as well as for prediction intervals for new observations in x. The assumption of normal distribution additionally helps avoid skewness and outliers, mean 0 guarantees a linear relationship. The constant variance, also called homoscedasticity, is also needed for inference (confidence intervals and tests). This assumption would be violated if the variance of y (which is equal to the residual variance a2, see below) is dependent on the value of x, a situation called heteroscedasticity, see Figure 4.8. 

Thereby we have to consider that the outlier test assumes the chosen approach for the regression function to be correct. First we should have a look on the plot of the residual analysis, because from there we can recognise potential outliers. We calculate the regression both with and without the potential outlier. Then we can apply either the F-test or the t-test... 

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. 

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 ... 

If the data as a whole appear normally distributed but there is concern that an extreme point is an outlier, it is not necessary to apply the Rankit procedure. The Grubbs s outlier test (1950) is now recommended for testing single outliers, replacing Dixon s Q-test. After identifying a single outlier, which, of course, must be either the maximum or minimum data value, the G statistic is calculated ... 

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