Two-sample plot

Typical two-sample plot when (a) random errors are larger than systematic errors due to the analysts and (b) systematic errors due to the analysts are larger than the random errors. 

Relationship between point In a two-sample plot and the random error and systematic error due to the analyst. 

A two-sample plot of the data is shown in Figure 14.19, with the average value for sample 1 shown by the vertical line at 245.9, and the average value for sample 2 shown by the horizontal line at 243.5. To estimate Grand and Gjys, it ... 

Two-sample plot for data In Example 14.7. The analyst responsible for each data point Is Indicated by the associated number. The true values for the two samples are Indicated by the. ... 

The two-sample plot for the data in Example 14.7 is shown in Figure 14.19. Identify the analyst whose work is (a) the most accurate (b) the most precise (c) the least accurate and (d) the least precise. 

Construct a two-sample plot for these data, and estimate values for Grand and O ys assuming a = 0.05. 

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 thermal conductivities of Ihe two samples, plotted in Figure 3, are very low at temperatures around 1000°C. As the Mg concentration increases, the thermal conductivity becomes lower. Low thermal conductivity coupled with low thermal expansion suggest that these compositions are resistant to thermal shock. The thermal conductivity of these compositions is noticeably lower than those of ZrOa, a common thermal barrier material. More samples are currently being evaluated and the effects of composition and density on thermal conductivity will be further established. 

The design of a collaborative test must provide the additional information needed to separate the effect of random error from that due to systematic errors introduced by the analysts. One simple approach, which is accepted by the Association of Official Analytical Chemists, is to have each analyst analyze two samples, X and Y, that are similar in both matrix and concentration of analyte. The results obtained by each analyst are plotted as a single point on a two-sample chart, using the result for one sample as the x-coordinate and the value for the other sample as the -coordinate. ... 

When two samples of air are brought together the condition of the mixture may be arrived at arithmetically by adding the heat flow of each and dividing by the total mass flow and similarly for the moisture flow. Alternatively, plot the condition of each onto a psychrometric chart. The mixed condition lies on a straight line between the two in a position proportional to the two quantities. 

E.33 Suppose that an element has two isotopes, one of mass mx and the other of mass m2, and that the former constitutes x% of the sample. Plot a graph showing how the mean mass of the atoms varies as x changes from 0% to 100%. 

If sample patterns in a large database are each defined by just two values, a two-dimensional plot may reveal clustering that can be detected by the eye (Figure 3.1). However, in science our data often have many more than two dimensions. An analytical database might contain information on the chemical composition of samples of crude oil extracted from different oilfields. Oils are complex mixtures containing hundreds of chemicals at detectable levels thus, tire composition of an oil could not be represented by a point in a space of two dimensions. Instead, a space of several hundred dimensions would be needed. To determine how closely oils in the database resembled one another, we could plot the composition of every oil in this high-dimensional space, and then measure the distance between the points that represent two oils the distance would be a measure of the difference in composition. Similar oils would be "close together" in space,... 

It is important to remember at this point that the metallicities for the two samples of stars plotted in Fig. 1 were derived using exactly the same techniques, and are thus both in the same scale (see [19]). Also, in the CORALIE planet search sample we have never used the stellar [Fe/H] as a criterion to chose a star. The comparison shown in Fig. 1 is thus not sample-biased. Finally, and as shown in [21], the precision in the derived radial-velocities is not a strong function of the stellar metallicity. The observed increasing frequency of planets with increasing [Fe/H] is thus also not due to any bias in the planet searches. 

Fig. 9. Arrhenius plots of the free hole concentration p (log p versus 1000/T) in two samples cut from a partially dislocated slice of ultra-pure germanium. The dislocation-free sample contains an acceptor with Ev + 80 meV. The shallow level net-concentration is the same in both samples.

Fig. 77, which plots the depth of shade of two P.O.34 samples versus the time needed to disperse the pigment, represents the dispersibility curve of two types with different particle size distributions. The two samples of Pigment Orange 34 are characterized in Figs. 70 and 71 (pp. 127 and 128). 

A two-component plot of the 13C/12C isotope ratio from the saturated and aromatic fractions of five samples previously identified (Table 4.8 and Figure 4.12) is pre-... 

FIGU RE 4.19 Two-component plot of the DIH ratio and 13C/12C isotope ratio for two LNAPL samples. 

The data were modeled by a principal components model with three components. The statistical results method (25. 31) are presented in Table IV and V. In addition, the measured total PCB concentration is included in Table IV. One of the three sets of two-dimension plots (Theta 1 vs Theta 2) is presented in Figure 10. Individual samples of a given Aroclor were distributed regularly in these plots and samples were ordered according to concentration. The sums of squares decreased from 4,360 to 52.4 (Table V.) and approximately 88 percent of the standard deviation was explained by the three term component model. 

All samples plot in the basalt to alkaline basalt fields of the Zr/Ti02 vs. NbA diagram of Pearce (1996) (Fig. 3). The NbA ratios define two distinct groups (1) tholeiitic metavolcanic rocks structurally underlying VMS mineralisation and (2) more alkaline ultramafic cumulates and metavolcanic rocks above VMS... 

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. 

The primary purpose of any quality control scheme is to identify ("flag") significant performance changes. The two-sample quality control scheme described above effectively identifies performance changes and permits separation of random and systematic error contributions. It also permits rapid evaluation of a specific analytical result relative to previous data. Graphical representation of these data provide effective anomaly detection. The quality control scheme presented here uses two slightly different plot formats to depict performance behavior. 

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-... 

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