Statistical tests Dixon test

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. 

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)... 

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. 

In this text we refer to the ISO recommended DIXON test, but note that other tests are available, along with tables, in the statistics literature (see, e.g., [MULLER et al., 1979]). 

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. 

Testing for an outlier under the assumption of normal distribution can be carried out by the Dixon s test. This test uses the range of measurements and can be applied even in cases where only few data are available. The n measurements are arranged in ascending order. If the very small value to be tested as an outlier is denoted by Xi and the very large striking value by x, then the test statistics is calculated by... 

Once a technical evaluation has been carried out, a statistical analysis is needed to confirm the absence of outlying means, examine the precision of the data, and evaluate the certified (or assigned) values and their uncertainties. A wide range of statistical tests exist in this respect they are based on the calculation of the mean values obtained by different laboratories and/or methods and a study of their distribution, and an analysis of the variances obtained. Examples are the Dixon (Nalimov) test for the evaluation of the... 

To prove that the outlier is outside the expected range of observations a statistical test may be of help. A common statistical approach may be to apply the Q-test of Dixon. Q is defined as the ratio of the deviation of the discordant value from its nearest neighbours with respect to the range of the values. 

Q Test statistic (estimate) of Dixon s outlier test (4.35)... 

The Q test, suggested by Dean and Dixon (1951) is statistically correct and valid, and it may be applied easily as stated below ... 

In Chapters III and IV, tables for estimating standard devistion from the range, and criteria for testing for extreme values are reproduced with permission of W.J. Dixon from Introduction to Statistical Analysis by Dixon and Massey (McGraw-Hill), and Criteria for Testing Extreme Mean by Dixon, Biometrics 9 (1953). 

Before we cover the various methods of determining whether differences in level exist between groups of data, a few words on the fundamental assumptions underlying these tests is in order, The concept of statistical inference is expressed very well by Dixon... 

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 ... 

During World War II Dixon and Mood [72] developed a special experimental method for testing the sensitiveness of explosives to impact. The method gave a statistical estimation of the mean value. It became known as the Bruceton up-and-down method. The primary advantage of the method is that it increases the accuracy with which the mean value can be economically determined. The method requires fewer tests than other methods. 

Sometimes, a value within a set might appear aberrant (this is known as an outlier). Although it might be tempting to reject this data point, it must be remembered that a value can only be aberrant relative to some law of probability. There is a simple statistical criterion on which to base the decision of whether to retain or reject this value. Dixon s test is based on the following ratio (as long as there are at least seven measurements) ... 

The methods of robust statistics have recently been used for the quantitative description of series of measurements that comprise few data together with some outliers [DAVIES, 1988 RUTAN and CARR, 1988]. Advantages over classical outlier tests, such as those according to DIXON [SACHS, 1992] or GRUBBS [SCHEFFLER, 1986], occur pri-marly when outliers towards both the maximum and the minimum are found simultaneously. Such cases almost always occur in environmental analysis without being outliers in the classical sense which should be eliminated from the set of data. The foundations of robust statistics, particularly those of median statistics, are described in detail by TUKEY [1972], HUBER [1981], and HAMPEL et al. [1986] and in an overview also by DANZER [1989] only a brief presentation of the various computation steps shall be given here. 

Dixon s test is a parametric test for detecting outliers. At least three results are needed. The dataset is arranged in order of increasing magnitude x1, x2...xn. Dixon s >-statistic is calculated. The equation depends on the number of results, g-statistic for three to seven observations ... 

TABLE 6.6. Critical Values for Dixon s Test. The Suspected Value is an Outlier if the Calculated 2-Statistic is Above the Critical Value... 

Some errors are unavoidable in impact sensitivity tests like the drop hammer test and drop ball test Important questions involve the precision and accuracy of acquired results. During the World War II in U.S.A., statistical investigations on drop hammer tests were carried out mainly by Professor Dixon 211 at the Bruceton Laboratory to achieve greater accuracy in determining impact sensitivity with the fewest trials. 

The Dixon Up-Down technique was first described in the statistical literature in 1947. It is designed to estimate an ED50 in clinical trials or toxicological tests, when a quantal response is measured (see Figure 9.1). However, it should be... 

In order to use Dixon s test for an outlier, that is to test Hq all measurements come from the same population, the statistic Q is calculated ... 

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