Repeatability standard deviation

Interpretation The model can only be improved upon if the residual standard deviation remains significantly larger (F-test ) than the experimental repeatability (standard deviation over many repeat measurements under constant conditions, which usually implies within a short period of time ). Goodness of fit can also be judged by glancing along the horizontal (residual = 0) and looking for systematic curvature. 

Sect. 7.1.3 —> Repeatability conditions include the same measurement procedure, the same observer, the same measuring instrument, used under the same conditions, the same location, and repetition over a short period of time — Repeatability standard deviation... 

The precision limits r and R are given by equations (4.3a) and (4.3b), respectively, where tv>a is the Student /-value for v degrees of freedom and a corresponds to the stated probability, sr is the repeatability standard deviation and Sr is the reproducibility standard deviation calculated from (v + 1) results ... 

If the analytical method used by participants in the proficiency testing round has been validated by means of a formal collaborative trial, then the repeatability and reproducibility data from the trial can be used. The repeatability standard deviation gives an estimate of the expected variation in replicate results obtained in a single laboratory over a short period of time (with each result produced by the same analyst). The reproducibility standard deviation gives an estimate of the expected variation in replicate results obtained in different laboratories (see Chapter 4, Section 4.3.3 for further explanation of these terms). 

If or represents the reproducibility standard deviation and ar represents the repeatability standard deviation, the between-laboratory standard deviation, CTl, is calculated from the following ... 

Repeatability standard deviation (,vr) (with the respective unit) Repeatability relative standard deviation (RSDr) (%)... 

Repeatability Standard Deviation Repeatability Limit r Reproducibility... 

If we don t have such an ideal control sample, but only one with a matrix different from the routine sample (e.g. a standard solution) than we have to consider also the uncertainty component arising from changes in the matrix. For this purpose we use the (repeatability) standard deviation calculated from repeated measurements of our routine samples (performed e.g. for a range control chart). When we estimate the reproducibility within laboratory we now have to combine both contributions by calculating the square root of the sum of squares. 

Calculated repeatability, intermediate precision, and reproducibility values can be compared with those of existing methods. If there are no methods with which to compare the precision parameters, theoretical relative reproducibility and repeatability standard deviations can be calculated from the Horwitz equation and the Horrat value (Table 5). Horwitz RSD values are reported in Table 6. Higher variability is expected as the analyte levels approach the detection limit (see below). Next to the Horwitz equation, the AOAC s Peer Verified Program proposes its own levels of acceptability of %RSD as a function of analyte concentration level [56,72]. 

When the repeatability standard deviation is known, it can be used to assess results done in duplicate. If the repeatability is Uj, then the 95% confidence interval of the difference of two results is... 

Use a top-down approach using reproducibility and repeatability standard deviations from an interlaboratory study by the Harmonized IUPAC/AOAC protocol (Horwitz 1995) or ISO 5725 (ISO 1994). 

A collaborative study for the determination of ethoxyquin in various meals and extruded pet foods was done under Schreier and Greene (134). Eleven laboratories took part in the study and determined ethoxyquin in acetonitrile extracts of ground samples using a column packed with C,8 octadecylsilane and a mixture of acetonitrile and ammonium acetate solution as a mobile phase. The method was tested for the analysis of 16 samples that contained ethoxyquin from 0.25 to 289 ppm. Repeatability standard deviations ranged from 0.08 to 3.2 ppm, and repeatabil-... 

The analytical method used, which involved sample extraction followed by cleanup and determination by gas chromatography (GC)/electron capture detection (ECD), had a repeatability standard deviation of 1.3 qg/kg therefore a contribution of at least -2.6 y/g/kg to the uncertainty (k=2) of the certified value must be expected when using this method to assess homogeneity. Such a value will make the major contribution to the total uncertainty (U) of the certified value, especially where the latter is based on high-accuracy IDMS measurements, which have an expanded uncertainty of only -0.7 y/g/kg (Table 2). 

From the results obtained the repeatability standard deviation Sr as well as the repeatability limit r can be calculated on a 95 % probability level according to Eq. (10-13). 

The results of the repeatability experiments can be used to calculate a standard deviation, which is often called the repeatability standard deviation. This value is useful in helping the analyst determine a repeatability limit - The value less than or equal to which the absolute difference between two test results... 

The analyst performs 10 measurements under repeatability conditions and has determined the repeatability standard deviation to be 0.12. 

According to ISO 5725 [7] the total mean X, the repeat standard deviation Sr, the between laboratory standard deviation 5 and the reproduce standard deviation Sr were determined. The relation is given by... 

The repeat standard deviation describes the scattering of the measuring results under repeat conditions (same laboratory, same equipment, same staff). Whereas, the between laboratory standard deviation expresses the differences between the laboratories. The reproduce standard deviation contains the two above mentioned scatter components. It is the deviation under reproduce conditions (different laboratories, different equipment, different staff). To get a unique repeat standard deviation it must be assumed that it does not vary (significantly) with the laboratory. For this reason the standard recommends a statistical outlier test (Cochran test) for the individual standard deviations of the laboratories. Furthermore, the individual laboratory means are a subject to an outlier test (Grubbs test). 

The mercury intrusion measurements were performed with a good precision within each individual laboratory (repeat standard deviation) as well as in different laboratories (reproduce standard deviation) for all mortar samples Bl, Gl, B2, G2, B3, G3. The reproduce standard deviations are 1.5 to 2 times higher than the repeat standard deviations. In particular cases,... 

The median pore radius does not show clear correlations to sample geometry (Table 3). The repeat standard deviations of the granules are a little smaller than that for the cylinders. 

Sr - relative repeatability standard deviation SR - relative reproducibility standard deviation [mg mL-1]... 

The repeatability standard deviation is defined as The precision of a method expressed as the standard deviation of independent determinations performed by a single analyst using the same apparatus and techniques. Hence the repeatability is what governs any replicate measurements made in your laboratory by you on the test material. The reference to independent measurements means that a number of separate test portions should be weighed, dissolved, and measured, not that the same solution should be presented to the... 

Returning to the practical problem of routine measurement, if a laboratory has established a reasonable estimate of the repeatability standard deviation, then the routine duplicate measurements may be checked against this value. Suppose the repeatability standard deviation is ot. The standard deviation of the difference between two measurements is J2ox and the 95% confidence interval on the expected difference of 0 is 1.96 x +J2ot = 2.8[Pg.65]

Hence from ANOVA we have estimates for the repeatability standard deviation (sr) and the standard deviation associated with the effect (,vc). 

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