Systematic differences between methods

H0 If Te is less than or equal to /-(able value, then there is NO SYSTEMATIC DIFFERENCE between method results. 

Another type of application of the t test is to individual differences between sets of observations. In Example 26-3 the same sample was analyzed by two methods. But we may wish to determine whether there is a systematic difference between methods A and B irrespective of the sample. Both methods are assumed to have essentially the same standard deviation that does not depend on the sample. The fourth column lists the differences between the two methods for the three tests common to both methods. The standard deviation of the differences is... 

Interpretation of Systematic Differences between Methods Obtained on the Basis of Regression Analysis... 

Once it has been established that methods correlate adequately, other actions may be required since there may still be systematic differences between methods,... 

In this example the variance due to systematic differences between the analysts is almost an order of magnitude greater than the variance due to the method s precision. 

Collaborative testing provides a means for estimating the variability (or reproducibility) among analysts in different labs. If the variability is significant, we can determine that portion due to random errors traceable to the method (Orand) and that due to systematic differences between the analysts (Osys). In the previous two sections we saw how a two-sample collaborative test, or an analysis of variance can be used to estimate Grand and Osys (or oJand and Osys). We have not considered, however, what is a reasonable value for a method s reproducibility. 

The test to determine whether the bias is significant incorporates the Student s /-test. The method for calculating the t-test statistic is shown in equation 38-10 using MathCad symbolic notation. Equations 38-8 and 38-9 are used to calculate the standard deviation of the differences between the sums of X and Y for both analytical methods A and B, whereas equation 38-10 is used to calculate the standard deviation of the mean. The /-table statistic for comparison of the test statistic is given in equations 38-11 and 38-12. The F-statistic and f-statistic tables can be found in standard statistical texts such as references [1-3]. The null hypothesis (H0) states that there is no systematic difference between the two methods, whereas the alternate hypothesis (Hf) states that there is a significant systematic difference between the methods. It can be seen from these results that the bias is significant between these two methods and that METHOD B has results biased by 0.084 above the results obtained by METHOD A. The estimated bias is given by the Mean Difference calculation. 

For the two studies compared in this paper, different measuring methods have been used. However, the systematic difference between the results from the two types of equipment can be estimated to be less than 20 %. 

Three methods for measuring Ar2+ have been described in the preceding examples. Two of the methods depend on a linkage relation (Eq. (21.30)) but find Kohs in different ways the third method is based on the direct measurement of r2+ for the two RNA conformations under consideration. The error bars in the Fig. 21.4D comparison of the sets of Ar2+ values illustrate the difficulty in quantitating Ar2+ very accurately by any method, but there are some systematic differences between the measurements (particularly at higher concentrations of Mg2+) which most likely reflect the different assumptions made by each method. Here we first summarize the assumptions that go into the formulas and analyses, and then comment on the merits and drawbacks of each approach. 

Competitive RIA and, lately, ELISA are the methods used to measure the serum concentration of these markers. Systematic differences between the RIA and ELISA in establishing PINP are explained by the existence of two molecular forms, and different antigenic reaction of the antibodies of both methods with them (J2, P7). 

Figure 14-24 Simulated comparison of two sodium methods. The solid line indicates the average estimated OLR line, and the dashed line is the identity line. Even though there is no systematic difference between the two methods, the average OLR line deviates from the identity line corresponding to a downward slope bias of about 10%.

A systematic difference between two methods is identified, if the estimated intercept differs significantly from zero, or if the slope deviates significantly from 1. This is decided on the basis of t-tests... 

Having estimated Aq and b, we have the estimate of the systematic difference between the methods, D at a selected concentration Xli ,rgctc... 

Various technologies have been used to measure plasma lipids and lipoproteins and lipoprotein subfractions, including enzymatic, immunochemical, and chemical precipitation reagents, and physical methods, such as ultracentrifugation, electrophoresis, column chromatography, and others. Such methods have been reviewed extensively. As mentioned earlier, however, the cholesterol content of any particular lipoprotein class can vaiy somewhat from individual to individual. Moreover, although different methods of lipoprotein separation may produce similar lipoprotein fractions, they usually do not produce identical fractions, giving rise to systematic biases between methods that purport to measure the same component. The present discussion focuses primarily on methods and procedures commonly used in clinical practice for lipid and lipoprotein measurements. 

Procedures applicable to correct for the systematic differences between XRD and ND derived ADPs are described in detail by Blessing [60]. One of the most appealing methods makes use of the linear correlation often found between the principal components of the MSDA tensors derived from the two types of experiments. The relationship obtained for the non-hydrogen atoms can be used to modify the ADPs of H-atoms from the ND experiment, thus allowing them for fixing in the refinement of the X-ray charge density. 

There may be cases where there are no systematic differences between predicted and experimental values, but where the scatter of the residuals depends on the value of the factor. This could be because the standard deviation is dependent on the response (see section 4). Otherwise, if this scatter of residuals proves not to be response-dependent, but a function only of the level of the factor, then the methods of section IV could prove useful for reducing the variability of the formulation or process being studied. 

Another reason that can account for the systematic differences between the values of A H (II), measured by the second-law and Arrhenius plot methods, and those of A H (III) measured by the third-law method, is the systematic decrease of the contribution of the condensation energy to the reaction enthalpy with increasing temperature and the ensuing slight increase of A H (III) and a substantially larger decrease of A H (II). This effect will be considered in detail in Sect. 8.2. 

However, as new approaches or new theories are developed, the solution of problems insoluble within the framework of traditional concepts is accompanied by appearance of new problems and enigmas. This approach is not an exception. In particular, the mechanism of the transfer of the condensation energy of the low-volatility product to the reactant and the effect of the S3mi-metry of the reactant crystal-lattice on the composition of the gaseous decomposition products remain unclear. To solve these problems on the basis of the new mechanistic and kinetic concepts discussed in this book, it would be appropriate to use the experience accumulated in solid-state physical chemistry and in crystal chemistry. The systematic differences between the enthalpies measured by the third-law method and those measured by the second-law and Arrhenius plot methods undoubtedly deserves a more thorough study. This problem is especially important for successful application to reactions involving the formation of solid products. 

This test is probably the most used of all statistical tests. It is very valuable when systematic differences between samples are caused by a single factor, and is entirely appropriate for comparing two independent averages. Arrhenius and Berzelius, however, made determinations on samples from five different vinegar producers. It is natural to suspect that these samples have different concentrations of acetic acid, and that samples from the same manufacturer are likely to be more similar to each other than to those coming from different producers. For this reason alone the results of the analyses are already expected to vary, blurring a possible difference in analytical technique. Since we are interested in a possible difference between the analysts, we need an improved method, which eliminates the variation caused by the different producers on the final result. 

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