Youden plots

The example demonstrates that all relevant information must be used ignoring the fact that the PM and HPLC measurements for / = 1. .. 5 are paired results in a loss of information. The paired data should under all circumstances be plotted (Youden plot. Fig. 2.1, and Fig. 1.23) to avoid a pitfall it must be borne in mind that the paired r-test yields insights only for the particular (addi-... 

Analysis of variance (ANOVA) tests whether one group of subjects (e.g., batch, method, laboratory, etc.) differs from the population of subjects investigated (several batches of one product different methods for the same parameter several laboratories participating in a round-robin test to validate a method, for examples see Refs. 5, 9, 21, 30. Multiple measurements are necessary to establish a benchmark variability ( within-group ) typical for the type of subject. Whenever a difference significantly exceeds this benchmark, at least two populations of subjects are involved. A graphical analogue is the Youden plot (see Fig. 2.1). An additive model is assumed for ANOVA. 

At least two parameters are tested by the same laboratory on many nominally similar samples. In both cases, the simplest outcome is a round patch in the Youden plot, see Fig. 2.1, of points that signifies just noise, no correlation. .. no participating laboratory (or sample or point in time) is exceptional. On the other hand, an elliptical patch, especially if the slope deviates from what could be expected, shows that some effects are at work that need further investigation. After just noise, the... 

Probability plot Q-Q plot P-P Plot Hanging histogram Rootagram Poissonness plot Average versus standard deviation Component-plus-residual plot Partial-residual plot Residual plots Control chart Cusum chart Half-normal plot Ridge trace Youden plot... 

What would the resulting Youden plots look like if the method was rugged If the method was not rugged If the laboratories were precise, but each was biased If the laboratories were imprecise, but accurate [See Youden (1959).]... 

A modified Youden two sample quality control scheme is used to provide continuous analytical performance surveillance. The basic technique described by other workers has been extended to fully exploit the graphical identification of control plot patterns. Seven fundamental plot patterns have been identified. Simulated data were generated to illustrate the basic patterns in the systematic error that have been observed in actual laboratory situations. Once identified, patterns in the quality control plots can be used to assist in the diagnosis of a problem. Patterns of behavior in the systematic error contribution are more frequent and easy to diagnose. However, pattern complications in both error domains are observed. This paper will describe how patterns in the quality control plots assist interpretation of quality control data. 

Youden described a plotting protocol that depicts the relative positions of individual runs on two samples. Consider the hypothetical case where an analytical method has been perfected and no sys-... 

Another graphical description of the data is used when comparing the results of several trials is the box plot (also called box-and-whisker plot). A box represents the range of the middle 50% of the data, and whiskers extend to the maximum and minimum values. A line is drawn at the median value. A glance a this plot allows one to assess the symmetry and spread of the data. Figure 5.4 is a box plot for the carbonate data of figure 5.2. Specific plots, such as Youden two-sample plots for method performance studies, are discussed below. 

The procedure requires that there are two different but similar samples of the material to be analysed. Each sample is analysed once by each laboratory in the trial. The method is illustrated by using a data set of % aluminium in two limestone samples (Y and T) for ten laboratories taken from ref. 58 and shown in Table 26. The Youden plot of these data is shown in Figure 35. 

Figure 35 Youden plot of % aluminium data for samples X and Y...

While the Youden plot (Figure 3) indicates that there is systematic error in the various laboratories, a test by Spearmans rank correlation coefficient (Table Vb) is ambiguous. The ranking is significant at the 0.05 level but not at the 0.01 level thus a correlation of the ranks of the laboratories such as we see here would appear less than five times in 100 by chance but more than one time in 100. I prefer to look at these results in terms... 

Figure 3. Youden plot (see Ref. 7) of copper content in sample 2 vs. copper content in sample 1. Each point corresponds to the two best estimates" of the copper contents from a particular laboratory, and the laboratory number is given next to the point. The indicated means are calculated in Table V. Laboratory results not included in the calculation of the means are marked with an asterisk. A 45° line (X = Y + K) has been drawn in to indicate the spread of values.

A reference method is one which after exhaustive investigation has been shown to have negligible inaccuracy in comparison with its imprecision [International Federation of Clinical Chemistry (IFCC), 1979]. With its comparison of inaccuracy and imprecision this definition clearly refers to the principles of quality control in clinical chemistry. Indeed, statistical models such as Youden plots are used to find out whether the error in a pair of results happens by chance (imprecision of the method) or is systematic (inaccuracy) (Youden, 1967). If the results are close to the true values, inaccuracy is negligible in comparison with imprecision. As demonstrated earlier, each analytical procedure has a certain degree of imprecision consequently, the total absence of systematic error can never be proved. Only as the influence of a systematic error is evident in comparison with the influence of chance or random error can the systematic error be demonstrated. 

Well-designed proficiency studies provide a good estimate of the method bias. Several protocols and statistical methodologies have been developed for assessing this bias, for example, ISO 5725-4 [28], International Harmonized Protocol for Proficiency studies [29], and Youden plot [30],... 

Analysis of systematic errors in the determination of hydrocarbons in water can be achieved by use of Youden plots after transformation of the results to an overall mean of Mtotal=0 and a standard deviation of Stotal=l (Fig. 3). Almost all laboratories are distributed around the 45° line indicating that most of the variation was systematic rather than random, particularly at higher mineral oil concentrations (sample pair S2/S4, Fig. 3B). Results located within the interval Mtotal 2 Stotal indicate sufficient proficiency of the participating laboratories in performing the determination of hydrocarbons in water... 

Fig. 3 Youden plot of the results (transformed to an overall mean of Mtotal=0 and a standard deviation of Stotal=l) for sample pair S1/S3 (A) and sample pair S2/S4 (B). Satisfactory performance is represented by the displayed box (Mtotal 2 Stotal). Each dot represents the results of an individual laboratory marked by a letter code ( - laboratories involved in PLC-4)...

Additional information about the nature of the systematic error is obtained when there are two different control materials analyzed by each laboratory. For example, the laboratory s observed mean for material A is plotted on the y axis versus its observed mean for material B on the x-axis these graphs are called Youden plots. Ideally the point for a laboratory should fall at the center of the plot. Points falling away from the center but on the 45° line suggest a proportional analytical error. Points falling away from the center but not on the 45° line suggest either an error that is constant for both materials or an error that occurs with just one material. 

A further assessment of the sets of data was carried out using a Youden s plot [4,5] which showed clearly the prevalence of systematic errors. However, As discussed below, these systematic errors were not statistically significant and no differences could be observed, on statistical grounds, between the different techniques used. 

The technical evaluation may also lead to the comparison of the results obtained from different methods. It will allow participants to extract information by comparing and possibly discussing their performance and method with other participants applying similar procedures, i.e. it may allow to discover biases in methods. If several enriched materials have been prepared and analysed the organiser may produce Youden plots where trends and systematic errors can appear [10-12]. Such more elaborated data presentations have to be issued with sufficient explanations to avoid misunderstanding and wrong conclusions. More advanced data treatment require the application of suitable robust statistics which have to be carefully chosen to arrive at sound scientific conclusions. Their meaning should always be explained and documented. 

The data should be reported as specified in the protocol with the requested significant figures. Valid data (those free of gross errors and produced following the protocol) should be submitted to various statistical treatment for outlier detection of mean and variance, and an ANOVA treatment to establish the repeatability and reproducibility figures. All these treatments and their sequence are specified in the lUPAC protocol [2]. The final report should contain all individual and statistical data additional graphical representation e.g. Youden-plots, bar-graphs etc may also be added. 

Fig. 12.4a. Youden plot of the determination of Al in marine sediments expressed as z-scores. The plot shows clear systematic differences due to the method of sample digestion. The group of lower (left) results was obtained by digestion methods which did not include any HF treatment e.g. nitric acid or aqua regia. The upper (right) group used an HF treatment or non-destructive methods e.g. XRF.

Fig. 12.4b. Youden plot of the determination of Cd in marine sediments, expressed as z-scores. The results show a mixture of both random (data far from the dotted line) and systematic errors. Most data are within Z < 2.

Fig. 12.5. Youden plot of a natural and a MeHg spiked raw extract of fish (adapted from ref[13]) The results obtained by each laboratory for sample A and B are reported on the horizontal and the vertical axis respectively. The intersection of both results is figured by the points in the graph. Dotted lines of the central square show the standard deviation of the mean of means. In an ideal case all laboratories should have their results in the square. Some sets of results are far from this point which demonstrates the presence of remaining systematic errors in these methods. Results far from the line show random errors.

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