Calibration curve statistics

One point of discussion is the number of necessary concentration points to construct calibration curves. Statistics demonstrated that it is not necessary to use more than six points. Because of the difficulty of handling carotenoid standards, a minimum coefhcient of correlation of 0.9 was suggested by Khachik et al.while Mantoura and Repeta recommended a coefficient above 0.95. The curves should intercept close to the zero value. 

If you already use a spreadsheet, you can skip this section. The computer spreadsheet is an essential tool for manipulating quantitative information. In analytical chemistry, spreadsheets can help us with calibration curves, statistical analysis, titration curves, and equilibrium problems. Spreadsheets allow us to conduct what if experiments such as investigating the effect of a stronger acid or a different ionic strength on a titration curve. We use Microsoft Excel in this book as a tool for solving problems in analytical chemistry. Although you can skip over spreadsheets with no loss of continuity, spreadsheets will enrich your understanding of chemistry and provide a valuable tool for use outside this course. 

The first question when dealing with a determination is what do we want to analyze Do we want a representative sample from an organ or do we want to find concentration differences within this organ This and related questions will be dealt in the first part of this chapter. The determination itself often requires a calibration curve statistics related to the bias, precision and detection limits will be dealt with in the second part. The third part is deals with data evaluation and concludes this chapter. 

Calibration curve data should be assessed to determine the appropriate mathematical regression that describes the instrument s response over the range of thecalibration curve (Section8.5). The report should include the back-calculated concentration values, accuracies, slopes, y-intercepts and correlation coefficients (R) and the coefficients of determination (R ) (Equation[8.18] in Section 8.3.1) for aU curves used in the validation. The value should be > 0.98 for each calibration curve. The R value (if used) must be > 0.99 for each calibration curve. An example table used to summarize the calibration curve statistics for each run used for method validation is shown as Table 10.2. 

Table 18. Statistical comparison (F-test [125]) of the methods. Standard deviation Sxo of the calibration curves for diethylstilbestrol and ethinylestradiol [114].

There are two statistical tests that should be applied to a calibration curve ... 

Calibration curve in spectrophotometry, 674, 753, 755, 800 statistical tests for, 144 Calmagite 318 Calomel electrode 63 forms of, 551 potential of, 554 preparation of, 551 Capacitative cell 527 Capacitance as an analytical tool, 528 Carbohydrates D. of hydroxyl groups in, (ti)) 306... 

A typical field test involves several steps (a) transporting the mobile unit to the site (b) instrument warmup (c) system check out, consisting of mobile unit measurements of distilled water and a 1-ppm stock phenol solution and (d) in situ measurements of the well water, repeated three times for statistical analysis. Signal levels recorded at a field site may be reported as equivalents of phenol (or other calibrant) using the calibration curves. Therefore, this method allows us to report the upper bounds of pollution levels. 

The quintessential statistical operation in analytical chemistry consists in estimating, from a calibration curve, the concentration of an analyte in an unknown sample. If the regression parameters a and b, and the unknown s analytical response y are known, the most likely concentration is given by Eq. (2.19), y being the average of all repeat determinations on the unknown. 

Two researchers prepare calibration curves. One researcher s curve has an r2 of 0.9977, the other an r2 of 0.9845. Which is the better calibration curve Explain how you came to this conclusion be specific. What statistics are better to use than r2 when assessing the quality of a calibration curve ... 

This requires calculations and/or the plotting of a calibration curve from which the desired results can be derived. Statistics are usually involved. 

Treatment of a real, imperfect calibration data set revealed the full complexity and breadth of the calibration curve -detection limit problem, ranging from varying statistical weights to an uncertain model and data containing possible blunders to an artificially imposed response threshold. 

The beauty of this completely random approach to the analyte detection limit is the direct applicability of the statistical hypothesis testing formalism. Also, long-term trends in calibration slope or backgrounds have little influence. One important assumption is made that the form of the calibration curve [Equation 2c] is fixed. Also, a subtle change has occurred, the operation is no longer linear, with A in the denominator. Thus, the distribution of x is only asymptotically normal, as the relative standard deviation of becomes smaller. 

The approximation for the variance of in (9b) holding when Vy is approximately constant. A summary of the application of Equation 9 to the linear calibration curve derived from known analyte concentrations x = (x-, X2. .. x ) and corresponding statistical weights (inverse variances) is given in Table II. 

Two procedures for improving precision in calibration curve-based-analysis are described. A multiple curve procedure is used to compensate for poor mathematical models. A weighted least squares procedure is used to compensate for non-constant variance. Confidence band statistics are used to choose between alternative calibration strategies and to measure precision and dynamic range. 

Calibration curve quality. Calibration curve quality is usually evaluated by statistical parameters, such as the correlation coefficient and standard error of estimate, and by empirical indexes, such as the length of the linear range. Using confidence band statistics, curve quality can be better described in terms of confidence band widths at several key concentrations. Other semi-quantitative indexes become redundant. Alternatively, the effects of curve quality can be incorporated into statements of sample analysis data quality. 

I have described a reasonably complete set of mathematical techniques for improving the precision of calibration-curve-based analyses and measuring their precision. Each technique may not be the optimum solution to each problem, but the overall philosophy should be correct. We should develop statistical techniques to measure precision which are self-consistent and... 

The limit of determination is commonly estimated by finding the intercept of extrapolated linear parts of the calibration curve (see point L.D. in fig. 5.1). However, it is often difficult to construct a straight line through the experimental potentials at low concentrations and, moreover, the precision of the potential measurement cannot be taken into consideration. Therefore, it has been recommended that, by analogy with other analytical methods, the determination limit be found statistically, as the value differing with a certain probability from the background [94]. 

This "secondary" molecular weight calibration curve was fit to a polynomial over the retention volume range of the sample. Then the molecular weight distribution statistics are calculated from this "secondary" calibration curve and the DRI trace of the sample under... 

To maintain consistency of statistical analyses, an identical microtiter plate setup was used by all participants, and all samples were analyzed in an identical manner. Both raw data and pretreated data from analyzed samples were submitted to OpdenKamp Registration and Notifieation for statistical evaluation. Data pretreatment consisted of all necessary calculations to convert the luminosity readings as submitted by the participating laboratories to effective dioxin-receptor activity (pM 2,3,7,8-TCDD TEQ). In addition to the analysis results of the defined samples (phase 1), the cleaned sediment extracts (phase 2), and the complete sediments (phase 3), all participants also submitted the results of the complete 2,3,7,8-TCDD calibration curves for statistical evaluation. 

Analysis of variance (ANOVA) analyses were performed using the general statistical package StatView 5.01 (SAS Institute, Cary, NC, USA). The ANOVAs were calculated as repeated-measures ANOVAs with wells as within factor for phase 1 and with plates as within factor for subsequent phases. Specialized statistics, such as comparison of fits of different calibration curves, were calculated in MATLAB 5.1 (MathWorks, Natick, MA, USA) using custom routines. 

Several overall conclusions can be drawn based on the statistical evaluation of the data submitted by the participants of the DR CALUX intra-and interlaboratory validation study. First, differences in expertise between the laboratories are apparent based on the results for the calibration curves (both for the curves as provided by the coordinator and for the curves that were prepared by the participants) and on the differences in individual measurement variability. Second, the average results, over all participants, are very close to the true concentration, expressed in DR CALUX 2,3,7,8-TCDD TEQs for the analytical samples. Furthermore, the interlaboratory variation for the different sample types can be regarded as estimates for the method variability. The analytical method variability is estimated to be 10.5% for analytical samples and 22.0% for sediment extracts. Finally, responses appear dependent on the dilution of the final solution to be measured. This is hypothesized to be due to differences in dose-effect curves for different dioxin responsive element-active substances. For 2,3,7,8-TCDD, this effect is not observed. Overall, based on bioassay characteristics presented here and harmonized quality criteria published elsewhere (Behnisch et al., 2001a), the DR CALUX bioassay is regarded as an accurate and reliable tool for intensive monitoring of coastal sediments. 

Statistical Analysis of NaDCC Calibration Curve Data... 

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