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The use of a sequence of experiments, where the design of each may depend on the results of previous experiments, including the possible decision to stop experimenting, is within the scope of sequential analysis, a field that was pioneered [12] by Abraham Wald in the context of sequential tests of statistical hypotheses. [13]
Experimental design is the design of all information-gathering exercises where variation is present, whether under the full control of the experimenter or an observational study. The experimenter may be interested in the effect of some intervention or treatment on the subjects in the design.
(where ! denotes factorial) possible run sequences (or ways to order the experimental trials). Because of the replication, the number of unique orderings is 90 (since 90 = 6!/(2!*2!*2!)). An example of an unrandomized design would be to always run 2 replications for the first level, then 2 for the second level, and finally 2 for the third level.
Experimental Design Diagram (EDD) is a diagram used in science to design an experiment.This diagram helps to identify the essential components of an experiment. It includes a title, the research hypothesis and null hypothesis, the independent variable, the levels of the independent variable, the number of trials, the dependent variable, the operational definition of the dependent variable and ...
Probabilistic design involving the use of probability in product and system design; System identification uses statistical methods to build mathematical models of dynamical systems from measured data. System identification also includes the optimal design of experiments for efficiently generating informative data for fitting such models. [11] [12]
Some of the basic theory of combinatorial designs originated in the statistician Ronald Fisher's work on the design of biological experiments. Modern applications are also found in a wide gamut of areas including finite geometry , tournament scheduling , lotteries , mathematical chemistry , mathematical biology , algorithm design and analysis ...
Mixture experiments are discussed in many books on the design of experiments, and in the response-surface methodology textbooks of Box and Draper and of Atkinson, Donev and Tobias. An extensive discussion and survey appears in the advanced textbook by John Cornell.
The seven basic tools stand in contrast to more advanced statistical methods such as survey sampling, acceptance sampling, statistical hypothesis testing, design of experiments, multivariate analysis, and various methods developed in the field of operations research. [10]