Can someone help me explain better the \"Youden measurement of uncertainty (Sm<S

Question

Can someone help me explain better the "Youden measurement of uncertainty (Sm<Ss/3)? " please

for random and t uncertainties, the overall standard deviation for an analytical measurement is related to the standard deviation of the sampling process and to the standard deviation of the method s by the relationship (8-1) In many cases, the method variance will be known from replicate measurements of a single laboratory sample. Under this circumstance, s, can be computed from mea- surements of so for a series of laboratory samples, each of which is obtained from several gross samples. An analysis of variance (see Section 7C) can reveal whether the between samples variation (sampling plus measurement variance) is significantly greater than the within samples variation (measurement variance) When s s/3, there is no point in trying to improve the measurement precision. Equation 8-1 shows that s, will be determined predominately by the sampling uncertainty under these conditions Youden has shown that, once the measurement uncertainty has been reduced to one third or less of the sampling uncertainty (that is, sms/3), further improvement in the measurement uncertainty is fruitless.2 This result suggests that, if the sampling ty is large and cannot be improved, it is often a good idea to switch to a less precise but faster method of analysis so that more samples can be analyzed in a given length of time. Since the standard deviation of the mean is lower by a factor of VN taking more samples can improve precision.

Explanation / Answer

From the point of definition of youden plot or curve we can simply say that the Youden plot is a graphical method to analyse inter-laboratory data, where all laboratories have analysed 2 samples. The plot visualises intra-laboratory variability as well inter-laboratory variability.

For the original Youden plot (Youden, 1959) (see Figure 1) the two samples must be similar and reasonably close in the magnitude of the property evaluated.

The axes in this plot are drawn on the same scale: one unit on the x-axis has the same length as one unit on the y-axis.

Each point in the plot corresponds to the results of one laboratory and is defined by a first response variable on the horizontal axis (i.e. run 1 or product 1 response value) and a second response variable 2 (i.e., run 2 or product 2 response value) on the vertical axis.

A horizontal median line is drawn parallel to the x-axis so that there are as many points above the line as there are below it. A second median line is drawn parallel to the y-axis so that there are as many points on the left as there are on the right of this line. Outliers are not used in determining the position of the median lines. The intersection of the two median lines is called the Manhattan median.

A circle is drawn that should include 95 % of the laboratories if individual constant errors could be eliminated.

A 45-degree reference line is drawn through the Manhattan median.

Points that lie near the 45-degree reference line but far from the Manhattan median, indicate large systematic error.

Points that lie far from the 45-degree line indicate large random error.

Points outside the circle indicate large total error.

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