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Hypothesis test outlier

There are statistical procedures available to choose models (hypothesis testing), assess outliers (or weight them), and deal with partial curves. [Pg.254]

Analytical methods are not ordinarily associated with the Neyman-Pearson theory of hypothesis testing. Yet, statistical hypothesis tests are an indispensable part of method development, validation, and use Such testa are used to construct analytical curves, to decide the "minimum significant measured" quantity, and the "minimum detectable true" quantity (33.34) of a method, and in handling the "outlier value problem"(35.36). [Pg.243]

As is common with all other hypothesis tests covered in this chapter, the calculated value of Q is compared with the appropriate critical value (shown in Table 2.3), and if the calculated value is greater than the critical value, the null hypothesis is rejected and the suspect data is treated as an outlier. Note that the result from the calculation is the modulus result (all negatives are ignored). [Pg.34]

Statistics such as the median and the trimmed mean are variously described as robust (i.e. suitable for use with a wide variety of population types) and/or resistant to outliers. Traditionally, robust and resistant statistics have been unpopular in classical statistics because it is often impossible to derive an analytical expression for the precision with which they can be estimated (i.e. formulae analogous to (4.7) above). This made it difficult to use the estimates in hypothesis tests. However, the advent of fast computers has radically altered the situation, since estimates of the precision of almost any ad hoc statistic can now be obtained by simulation tech-... [Pg.127]

To apply a significance test, a hypothesis must be clearly stated and must have a quantity with a calculated probability associated with it. This is the fundamental difference between a hunch and a hypothesis test—a quantity and a probability. The hypothesis will be accepted or rejected on the basis of a com-oarison of the calculated quantity with a table of values relating to a normal istribution. As with the confidence interval, the analyst selects an associated e/el of certainty, typically 95%. The starting hypothesis takes the form of the null hypothesis Hq. "Null" means "none," and the null hypothesis is stated in such a way as to say that there is no difference between the calculated quantity and the expected quantity, save that attributable to normal random error. As regards to the outlier in question, the null hypothesis for the chemist and the trainee states that the 11.0% value is not an outlier and that any difference... [Pg.27]

Grubbs test A hypothesis test to identify outliers. [Pg.620]

When the excitations are random, the peak indicators behave like random variables. They will therefore follow a statistical distribution which can be inferred from several undamaged samples. Many tools have been developed to detect a change in that statistical distribution such as outlier analysis or hypothesis testing. In this contribution, control charts (Montgomery 2009 Ryan 2000) are presented. This tool of statistical quality control plots the features or quantities representative of their statistical distribution as a function of the samples. Different univariate or multivariate control charts exist but all these control charts are based on the same principle which is summarized in Fig. 5. [Pg.3351]

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. [Pg.93]

The hypothesis we propose to test is that 71 ng/g is not an outlier in this data. Using the Dixon Q test, we obtain the following result ... [Pg.34]

What is unique about the use of the Grubbs tests is that, before the tests are applied, data are sorted into ascending order. The test values for G G2, and G3 are compared with values obtained from tables (see Table 2.4), as has been common with all the tests discussed previously. If the test values are greater than the tabulated values, we reject the null hypothesis that they are from the same population and reject the suspected values as outliers. Again, the level of confidence that is used in outlier rejection is usually at the 95 and 99% limits. [Pg.35]

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... [Pg.124]

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... [Pg.3]

This test is also based on the assumption of a normally distributed population. It can be applied to series of measurements (3-150 measurements). The null hypothesis that x is not an outlier within the measurement series of n values is accepted at level a, if the test quantity T is... [Pg.43]

The QQ-plots displayed in Figure 2.16b suggest a good fit to the normal distribution. However, the multivariate Jarque-Bera-test rejects the normality hypothesis (at a 5% a-level). This result is probably caused by some fluctuations in the outflow rates occurring at changes of the production level (e.g. see time intervals jO-70, 100-170 and 270-310). These outliers might be caused either by process instabilities or measurement errors. It is to conjecture that a better fit to the normal distribution can be achieved by explicitly... [Pg.46]

While the estimates of the autocorrelation coefficients for the Cg time series (lower rows in 1 to ordy change slightly, the estimates the autocorrelation coefficients for the Benzene time series (upper rows in to 3) are clearly affected since three parameters are dropped from the model. The remaining coefficients are affected, too. In particular, the lagged cross-correlations to the Cg time series change from 1.67 to 2.51 and from -2.91 to -2.67 (right upper entries in 1 and This confirms the serious effect of even unobtrusive outliers in multivariate times series analysis. By incorporating the outliers effects, the model s AIC decreases from -4.22 to -4.72. Similarly, SIC decreases from -4.05 to -4.17. The analyses of residuals. show a similar pattern as for the initial model and reveal no serious hints for cross- or auto-correlation. i Now, the multivariate Jarque-Bera test does not reject the hypothesis of multivariate normally distributed variables (at a 5% level). The residuals empirical covariance matrix is finally estimated as... [Pg.49]

With the hypothesis and confidence level selected, the next step is to apply the chosen test. For outliers, one test used (perhaps even abused) in analytical chemistry is the Q or Dixon test ... [Pg.29]

In the realm of statistical significance testing, there are typically several tests for each type of hypothesis. The Grubbs test, recommended by the International Standards Organization (ISO) and the American Society for Testing and Materials (ASTM), is another approach to the identification of outliers ... [Pg.29]


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