Randomization, experimental design

A sample may mis-estimate the population mean as a result of bias or random sampling error. Bias is a predictable over- or under-estimation, arising from poor experimental design. Random error arises due to the unavoidable risk that any randomly selected sample may over-represent either low or high values. 

In the two-sample collaborative test, each analyst performs a single determination on two separate samples. The resulting data are reduced to a set of differences, D, and a set of totals, T, each characterized by a mean value and a standard deviation. Extracting values for random errors affecting precision and systematic differences between analysts is relatively straightforward for this experimental design. 

V. L. Anderson and R. A. McLean, Design of Experiments—A Eea/istic Approach, Marcel Dekker, New York, 1974. This book provides an extensive exposition of experimental design at a relatively elementary level. It includes most of the standard material, as well as detailed discussions of such subjects as nested and spHt-plot experiments. Restrictions on randomization receive special emphasis. 

D. R. Cox, P/anning of Experiments,]ohxi Wiley Sons, Inc., New York, 1958. This book provides a simple survey of the principles of experimental design and of some of the most usehil experimental schemes. It tries "as far as possible, to avoid statistical and mathematical technicalities and to concentrate on a treatment that will be intuitively acceptable to the experimental worker, for whom the book is primarily intended." As a result, the book emphasizes basic concepts rather than calculations or technical details. Chapters are devoted to such topics as "Some key assumptions," "Randomization," and "Choice of units, treatments, and observations."... 

There is nothing that says we must slavishly follow one of the structured or random experimental designs. For example, we might wish to combine the features of structured and random designs. Also, there are times when we have... 

Experimental design, 27 manual, 32 random, 31 structured, 29 TILI, 33... 

Soybean bloassays of root exudates. Four soybean seeds ( Bragg ) were planted In each of 100 12.5 cm plastic pots filled with an artificial soil mix consisting of perlite/coarse sand/coarse vermiculite 3/2/1 by volume. After one week the plants were thinned to two per pot and the treatments were begun. The experimental design was a completely randomized design with 10 replications (pots) per treatment. On the first day of each week each pot was watered with 300 ml effluent from the appropriate growth units. On the fifth day of each week all pots were watered with Peter s Hydro-sol solution with CaCNOj. At other times the pots were watered as needed with tap water. On the second and fifth day of each week the height of the soybeans (base to apical bud) was measured. 

Root elongation bloassay of root exudates. Five ml aliquots of the root exudates were pipetted onto three layers of Anchor1 germination paper In a 10 by 10 by 1.5 cm plastic petri dish. Twenty five radish or tomato seeds were placed in a 5x5 array in each petri dish. Radish seeds were incubated at 20C for 96 hours tomato seeds were incubated at 20C for 168 hours, before the root length was measured. Experimental design was a completely randomized design with three replications (dishes) per treatment per bioassay seed species. The bioassay was repeated each week for 23 weeks. 

The experimental design was a randomized complete block with eleven treatments, two soybean varieties and five blocks (reps). The experiment was conducted six times at two week intervals, starting four weeks after the weeds were planted in the pipes. 

Statistical experimental design is characterized by the three basic principles Replication, Randomization and Blocking (block division, planned grouping). Latin square design is especially useful to separate nonrandom variations from random effects which interfere with the former. An example may be the identification of (slightly) different samples, e.g. sorts of wine, by various testers and at several days. To separate the day-to-day and/or tester-to-tester (laboratory-to-laboratory) variations from that of the wine sorts, an m x m Latin square design may be used. In case of m = 3 all three wine samples (a, b, c) are tested be three testers at three days, e.g. in the way represented in Table 5.8 ... 

In contrast to common statistical techniques, by modern experimental design influencing factors are studied simultaneously (multifactorial design, MFD). The aim of MFD consists in an arrangement of factors in such a way that their influences can be quantified, compared and separated from random variations. 

The reliability of multispecies analysis has to be validated according to the usual criteria selectivity, accuracy (trueness) and precision, confidence and prediction intervals and, calculated from these, multivariate critical values and limits of detection. In multivariate calibration collinearities of variables caused by correlated concentrations in calibration samples should be avoided. Therefore, the composition of the calibration mixtures should not be varied randomly but by principles of experimental design (Deming and Morgan [1993] Morgan [1991]). 

Eight Certified Reference Materials (CRMs) (Table 1) were analyzed, in triplicate random order, for 53 elements by five digestion protocols (Table 2) as shown in the experimental design (Table 3). All final determinations were by ICP-AES and -MS in a single batch using a randomized ordering of the prepared digestions. 

Random gene insertion, 72 453 Randomization, 5 388-389 70 811-813 commercial experimental design software compared, 8 398t Randomly oriented thin film model,... 

The four basic statistical principles of experimental design are rephcation, randomization, concurrent ( local ) control and balance. In abbreviated form, these may be summarized as follows. 

Random allocation of animals to treatment groups is a prerequisite of good experimental design. If not carried out, one can never be sure whether treatment-... 

Methodological controls. Some published studies on the effectiveness of hypericum have experimental design flaws, but there are several that are methodologically controlled, employing double-blind, randomization, and placebo controls. Randomized, placebo-controlled studies were summarized and evaluated in a meta-analysis by Linde and colleagues (1996). The combined subject pool was 1,757 outpatients with mild to... 

Dejaegher, B., Capron, X., Smeyers-Verbeke, J., and Vander Heyden, Y. (2006). Randomization tests to identify significant effects in experimental designs for robustness testing. Anal. Chim. Acta 564, 184-200. 

The nine distinctly different factor combinations in Figure 13.13 were obtained from a random number generator. In this sense, the experimental design in Figure... 

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