Application of statistical tests

The Reliability of Measurements. The Analysis of Data. The Application of Statistical Tests. Limits of Detection. Quality Control Charts. Standardization of Analytical Methods. 

One can consider the application of statistical tests and chemometric tools to be somewhat akin to torture—if you perform it long enough your data will tell you anything you wish to know—but most results obtained from torturing your data are likely to be very unstable. A light touch with the correct tools will produce a much more robust and useable result then heavy-handed tactics ever will. Statistics, like torture, benefit from the correct use of the appropriate tool. 

The reliability of measurements. The arrptysis of data. The application of statistical tests. Limits of detection. Quality control charts. Standardization of analytical methods. Chcmometrics. 

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. 

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. 

Finally, a word of caution (which should be self-evident) before estimating the calibration function by regression and the application of statistical tests, we must verify that the instrument is operating correctly. It may well happen that instrumental drifts or instrumental problems with lamps, monochromators, automatic pipettes, etc. cause serious problems that would show up unduly in the calibration function. ... 

This statistic is normal. As with the global test, the constraint test is based on the actual measurements before reconciliation. Reconciliation is not required in advance of the application of this test. Also, the... 

Different tests for estimation the accuracy of fit and prediction capability of the retention models were investigated in this work. Distribution of the residuals with taking into account their statistical weights chai acterizes the goodness of fit. For the application of statistical weights the scedastic functions of retention factor were constmcted. Was established that random errors of the retention factor k ai e distributed normally that permits to use the statistical criteria for prediction capability and goodness of fit correctly. 

A convenient size for a circular coupon is 3 8 cm dia., a thickness of 0 - 32 cm and a central hole of 1 1 cm. Although inherent in the philosophy of corrosion testing, the use of coupons with surfaces that simulate those in service has been found to be unsatisfactory owing to irreproducibility, and the standard procedure normally adopted is to abrade down to 120-grit. ASTM Method G4 1984 gives details of preparation of specimens, evaluation of replicate exposures and the application of statistical methods. 

The relative error is the absolute error divided by the true value it is usually expressed in terms of percentage or in parts per thousand. The true or absolute value of a quantity cannot be established experimentally, so that the observed result must be compared with the most probable value. With pure substances the quantity will ultimately depend upon the relative atomic mass of the constituent elements. Determinations of the relative atomic mass have been made with the utmost care, and the accuracy obtained usually far exceeds that attained in ordinary quantitative analysis the analyst must accordingly accept their reliability. With natural or industrial products, we must accept provisionally the results obtained by analysts of repute using carefully tested methods. If several analysts determine the same constituent in the same sample by different methods, the most probable value, which is usually the average, can be deduced from their results. In both cases, the establishment of the most probable value involves the application of statistical methods and the concept of precision. 

Life is a complicated affair otherwise none of us would have had to attend school for so long. In a similar vein, the correct application of statistics has to be learned gradually through experience and guidance. Often enough, the available data does not fit simple patterns and more detective work is required than one cares for. Usually a combination of several simple tests is required to decide a case. For this reason, a series of more complex examples was assembled. The presentation closely follows the script as the authors experienced it these are real-life examples straight from the authors fields of expertise with only a few of the more nasty or confusing twists left out. 

Prediction of the useful life, or the remaining life, of coatings from physical or analytical measurements presents many problems in data analysis and interpretation. Two important considerations are that data must be taken over a long period of time, and the scatter from typical paint tests is large. These considerations require innovative application of statistical techniques to provide adequate prediction of the response variables of interest. 

Before collecting data, at least two lean/rich cycles of 15-min lean and 5-min rich were completed for the given reaction condition. These cycle times were chosen so as the effluent from all reactors reached steady state. After the initial lean/rich cycles were completed, IR spectra were collected continuously during the switch from fuel rich to fuel lean and then back again to fuel rich. The collection time in the fuel lean and fuel rich phases was maintained at 15 and 5 min, respectively. The catalyst was tested for SNS at all the different reaction conditions and the qualitative discussion of the results can be found in [75], Quantitative analysis of the data required the application of statistical methods to separate the effects of the six factors and their interactions from the inherent noise in the data. Table 11.5 presents the coefficient for all the normalized parameters which were statistically significant. It includes the estimated coefficients for the linear model, similar to Eqn (2), of how SNS is affected by the reaction conditions. 

Statistical principles should be applied to the planning and analysis of all test programmes. Details of commonly needed techniques are given in a series of ISO standards as well as in standard text books. An alternative is BS 903 Part 2, Guide to the application of statistics to rubber testing , which includes the basics of design of experiments and has a bibliography [3]. 

BS 903-2, Physical testing of rubber. Guide to the application of statistics to rubber testing, 1997. 

Thus, when a property of the sample (which exists as a large volume of material) is to be measured, there usually will be differences between the analytical data derived from application of the test methods to a gross lot or gross consignment and the data from the sample lot. This difference (the sampling error) has a frequency distribution with a mean value and a variance. Variance is a statistical term defined as the mean square of errors the square root of the variance is more generally known as the standard deviation or the standard error of sampling. 

To test the applicability of statistical techniques for determination of the species contributions to the scattering coefficient, a one-year study was conducted in 1979 at China Lake, California. Filter samples of aerosol particles smaller than 2 ym aerodynamic diameter were analyzed for total fine mass, major chemical species, and the time average particle absorption coefficient, bg. At the same time and location, bgp was measured with a sensitive nephelometer. A total of 61 samples were analyzed. Multiple regression analysis was applied to the average particle scattering coefficient and mass concentrations for each filter sample to estimate aj and each species contribution to light scattering, bgn-j. Supplementary measurements of the chemical-size distribution were used for theoretical estimates of each b pj as a test of the effectiveness of the statistical approach. 

The goal of the year-long study at China Lake was to test the applicability of statistical techniques to determine the aerosol species contributions to the scattering coefficient. 

For many reasons, not least the influence of the quality movement and the widespread availability of personal computers, statistical methods are now much more widely appreciated and more frequently applied to the results of rubber tests. Also, a practical reason for not now needing a statistics chapter is the existence of the comprehensive British Standard Application of Statistics to Rubber Testing1 which at the time of writing is being considered for adoption as an ISO standard. It contains references to standards on statistical methods and also has a small bibliography. 

SCI WGI Industrial, chemical and oil hoses SCI WG2 Automotive hose SCI WG3 Hydraulic hose SCI WG4 Hose test methods SC2 Physical and Degradation Tests SC2 WGI Physical properties SC2 WG2 Viscoelastic properties SC2 WG3 Degradation tests SC2 WG4 Application of statistical methods... 

---