Design nested

Two Experimental versus control subjects One-at-a-time designs Factorial designs Fractional factorial designs Nested designs Special designs... 

The last of the major varieties of experimental design are the nested designs, where the levels of one factor are nested within (or are subsamples of) another factor. That is, each subfactor is evaluated only within the limits of its single larger factor. 

The analyst should avoid creating impossible factor combinations. This occurs, for instance, when choosing both the batch number and the manufacturer of the capillary as factors in a robustness test by means of a two-level design. It is impossible to define two unique batch numbers that exist for both manufacturers. The way to examine both factors is by using nested designs. ... 

RUGGEDNESS TESTING OF NON-PROCEDURE RELATED FACTORS THE USE OF NESTED DESIGNS... 

To study such factors one can use a nested design and interpret the results with a nested or hierarchic ANOVA. An example of a nested design is shown in Figure 3.5 and the ANOVA table for it is given in Table 3.30. The designs and ANOVA are called nested because the subordinate classification is nested within the higher level of classification. An example from practice of nested ANOVA is given by Wemimont [45]. 

The nested designs can be used to perform a ruggedness test following the definition of the US Pharmacopeia [7] or the second level requirements of the Canadian Acceptable Methods [14]. However, to our knowledge this methodology has not been applied yet for this purpose. 

Finally, there are two families of factorial designs which depend on the combination mode of the factors. If it is possible to combine each level of one factor with each level of every other factor this is denoted cross-classified design. The second family consists of nested designs or hierarchical experiments. In those designs the levels of one factor may not be combined with all the levels of another factor. As an example consider an investigation performed by two laboratories (factor no. 1) which unfortunately cannot... 

Wernimont reported an example of a nested design, which is an example of fractional replication. It was desired to evaluate an interlaboratory study of a method of acetyl determination. Results obtained by two analysts in each of eight laboratories were compared by having each analyst perform two tests on each of 3 days. The design was... 

An important extension of our large validation studies involves the use of data bases from field studies in the development of improved statistical methods for a variety of problems in quantitative applications of immunoassays. These problems include the preparation and analysis of calibration curves, treatment of "outliers" and values below detection limits, and the optimization of resource allocation in the analytical procedure. This last area is a difficult one because of the multiple level nested designs frequently used in large studies such as ours (22.). We have developed collaborations with David Rocke and Davis Bunch (statisticians and numerical analysts at Davis) in order to address these problems within the context of working assays. Hopefully we also can address the mathematical basis of using multiple immunoassays as biochemical "tasters" to approach multianalyte situations. 

Fig. 4.10a. One stage nested design. Each laboratory receives only one bottle of material and performs several measurements on them (2 in this case). This design does not allow one to test the between-bottle homogeneity within one laboratory and reduces the bclwccn-laboralory input.

Fig. 4.10b. Two stage nested design of an interlaboratory study allowing the verification of the homogeneity of the RM. (L laboratory number 1 to i, S sample bottle number 1 or 2 of laboratory i, X test sample of bottle 1 or 2 of laboratory i). In total 2i bottles are used, and in total 4i measurements are performed. If the tested bottles are selected regularly during the filling procedure, a good estimate of the between-bottle homogeneity can be given.

Fig. 4,11, Bar-graph presentation of results obtained in the certification of lead in mussel tissue BCR-CRM 278. The horizontal dotted line signifies the standard deviation of the set of data and the vertical dotted line the certified value (mean of means). The figure shows the that the SD of the DPASV and of the AAS methods are much larger than those obtained with IDMS. These differences would influence the evaluation of the homogeneity of the material through a two-stage nested design as proposed by ISO Guide 35.

A nested design, which is sometimes referred to as a hierarchical design, is used for an experiment in which there is an interest in a set of treatments and the experimental units are subsampled (Fig. 9.4). It has become a practical design or an approach to study and to evaluate method performance criteria that include accuracy expressed as overall recovery, intermediate precision, and... 

Analysis of variance (ANOVA) is also a common parametric statistic for comparing data from more than two groups [2]. There are a number of variants of this model, depending upon the number and combination of groups, categories, and levels one desires to evaluate. Common ones include one-factor, two-factor, and three-factor designs, as well as crossover and nested designs. 

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