Between sample variation

On the eighteenth day the analysis of variance and the standard deviation presented in Table III show that the between samples variation was dominant and remained so throughout the season. 

The principle of PCA consists of finding the directions in space—known as principal components (PCs)—along which the data points are furthest apart. It requires linear combinations of the initial variables that contribute most to making the samples different from each other. PCs are computed iteratively, with the first PC carrying the most information, that is, the most explained variance, and the second PC carrying most of the residual information not taken into account by the previous PC, and so on. This process can go on until as many PCs have been computed as there are potential variables in the data table. At that point, all between-sample variation has been accounted for, and the PCs form a new set of axes having two... 

In many cases, the method variance will be known from replicate measurements of a single laboratory sample. Under this circumstance, can be computed from measurements of 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). 

The overall S estimate. Use all the data together to calculate an overall standard deviation. This estimate of S will be inflated by the between-sample variation. Thus, it is an upper bound for S. If there are changes in process level, compute S for each segment separately, then combine them by using... 

This method of estimating al is not used in the analysis because the estimate depends on both the within- and between-sample variations. However, there is an exact algebraic relationship between this total variation and the sources of variation which contribute to it. This, especially in more complicated ANOVA calculations, leads to a simplification of the arithmetic involved. The relationship between the sources of variation is illustrated by Table 3.4, which summarizes the sums of squares and degrees of freedom. It will be seen that the values for the total variation given in the last row of the table are the sums of the values in the first two rows for both the sum of squares and the degrees of freedom. This additive property holds for all the ANOVA calculations described in this book. 

Statistical analysis of the data in Table II shows no significant difference between varieties or between positions on the tree. The average parathion residue on all varieties is equal to or slightly less than the variation between samples. 

It is inversely related to D and clearly cannot be greater than 1. Distances are measured from the point of application of the sample. As both /R and R( are related to D they will depend on the conditions under which a chromatogram is run. Valid comparisons between samples and between samples and standards can be made only if experimental conditions are identical. In many cases this is difficult to achieve and it is common practice to run samples and standards sequentially or simultaneously to minimize the effects of variations. 

Although laser ablation is clearly becoming more popular (as shown in Fig. 9.1), it is difficult to produce fully quantitative data because of problems in matrix matching between sample and standard (see below and Section 13.3). There are also likely to be variations in ablation efficiency in multi-component mixtures, leading to over- or under-representation of particular phases of the sample. It is also unlikely that all ablation products will enter the plasma in the elemental state, or that different particle sizes produced by ablation will have the same compositions. Ablation products may, therefore, not be truly representative of the sample (Morrison et al. 1995, Figg et al. 1998). Additionally, limits of detection for most elements are approximately... 

The results of interlaboratory study II are presented in Fig. 4.5.1. Five sets of results were obtained for the LAS exercise, and four sets for the NPEO exercise. For LAS, the within-laboratory variability ranged between 2 and 8% (RSD) for sample III (distilled water spiked with lmgL-1 LAS), 1 and 13% for sample 112 (wastewater influent), and 3 and 8% for sample 113 (sample 112 spiked with lmgL-1 LAS). Between-laboratory variations (calculated from the mean of laboratory means, MOLM) amounted to RSDs of 15, 30 and 30% for samples III, 112 and 113, respectively. The LAS values reported were in the range of 700—1100 p,g L-1 in sample III, 1100-1800 p,g L-1 in sample 112 and 1900-3000 p,g L-1 in sample 113, indicating that even in the matrix wastewater influent, the spiked concentration of lmgL-1 LAS could be almost quantitatively determined by all laboratories. 

Molecular phylogeny is a discipline that studies species differences between DNA or protein sequences. Its basic tenet is that during evolution, the sequences have drifted apart by mutation and selection as well as by random drift and fixation of variants in certain positions. The earlier two species separated the more differences became fixed. Phylogenetic trees are constructed on the basis of mutual differences of protein and/or DNA sequence. Comparison of intraspecies variation with between-species variation may in the future yield information on the neutralist/selectionist alternative. McDonald and Kreitman (1991) devised an interesting test against neutrality that compared the ratio of silent/replacement mutation of a given locus within a species with the same ratio between two related species. Under the neutral theory this should be equal (corrected for sample size), but in fact it is not (see Li, 1997, and Hudson, 1993, for a discussion). 

Figure 4.20. Variation of the molar ellipticity [0] and torsion constant a of pUC8 dimer with superhelix density. All samples were prepared from the same stock solution as described in the text. Solution conditions were 10 mM NaCl, 10 mM Tris, 1 mM EDTA, and pH 8, and the DNA concentrations were between 40 and 50 g/ml. , Five days after preparation +, 15 days after preparation , 2 months after preparation , samples prepared from the same initial stock solution 4 months after the other samples and measured within 5 days. Top [0] versus superhelix density a. Only the a = -0.015 sample changed significantly over the first few weeks. Bottom a versus superhelix density. Torsion constants are averages for 70- and 120-ns time spans. For the FPA measurements only, ethidium was added to a concentration of 1 dye per 300 base pairs. With the exception of a - - 0.025, the samples denoted by did not change significantly over a period of 2 months, and it is the final values that are plotted. The final measurement for the a= -0.025 sample is denoted by . The error bars are less than or equal to the size of the symbols in the figure. Complete data for o= —0.048 and o= —0.031 are given in Figure 4.10, which demonstrates the ability of FPA measurements to distinguish between samples whose torsion constants differ by only 10%.

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