Grubb’s test

This Grubbs s test is appropriate only for single outliers. Grubbs also published a test for a pair of outliers at either end of the data. The test statistic is the ratio of the sum of squared deviations from the mean for the set minus the pair of suspected outliers and the sum of squared deviations from the mean for the whole set ... 

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. 

The above analysis assumes that the results are normally distributed and without outliers. A Cochran test for homogeneity of variance and Grubbs s tests for single and paired outliers is recommended (see chapter 2). Data from... 

First test the data for outliers. This is not as straightforward as performing a Grubbs s test for replicates of a measurement on a single analyte. Because... 

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... 

Quantity Attribute or phenomenon, body or substance that may be distinguished qualitatively and determined quantitatively. (Section 1.4) Q-test (Dixon s Q-test) An outlier test. Grubbs s test is the preferred test to use. (Section 3.5)... 

How do I determine whether a datum is an outlier Perform a Grubbs s test. (Section 3.5)... 

How many data can I assign as outliers using the Grubbs s test given in chapter 3 ... 

Only one. There is a Grubbs s test for pairs of outliers (Massart et al.—see Bibliography). Any more and you should be asking yourself whether the data is normally... 

However, it is also useful to have a quick method to decide whether a particular value is an outlier or not. The method recommended by ISO is Grubbs s test, although many older texts still present Dixon s... 

G can be compared to tables of critical values for G at a = 0.05, critical, calculated using equation 3.2 below. If G > Gcvmca then the suspect point is rejected. Note that in the case of Grubbs s test, we compare with tabulated critical values simply because the calculation of the probability associated with the value of G is nontrivial. We do have a formula for the calculation of Gcriticai-... 

Table 3.2 Values of C7criticai used for Grubbs s test for outliers...

A query that may arise is if there are potential outliers at each end of the data what should we do The answer is that Grubbs s test is only for a single outlier. 

A common question is can you then perform an outlier test on the next furthest value from the mean Ideally Grubbs s test is for one potential outlier only, although it is quite common to see the test then used on the next potential outlier. One must be careful, however, as if you start to reject too many points in a small data set (say less than 10 values) then it is likely that the data are not normally distributed. 

Figure 3.7 Results from the measurement of fluoride in toothpaste. Data 1-9 are replicate measurements. Dashed lines are 95% confidence intervals. The circled datum (number 3) is the suspect outlier. The dotted line is the critical x value calculated from the a = 0.05", n = 9 Grubbs s test. The datum numbered 12 (circled cross) is the reference value of the sample (0.033 m/m%).

Table A.3 Values of C Criticai used for Grubbs s test for outliers, calculated as = (n - 1 )/SQRT(n) SQRT((TINV(a/n, n - 2))A2l(n - 2 + TINV(a/n, n - 2)A2)) ...

Notation Critical values for Grubb s test, single largest or smallest outlier, n = 4 1%—1.496, 5%—1.481. 

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