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Plackett–Burman designs are experimental designs presented in 1946 by Robin L. Plackett and J. P. Burman while working in the British Ministry of Supply. [1] Their goal was to find experimental designs for investigating the dependence of some measured quantity on a number of independent variables (factors), each taking L levels, in such a way as to minimize the variance of the estimates of ...
Design and Analysis of Experiments. Handbook of Statistics. Vol. 13. North-Holland. ISBN 978-0-444-82061-7. "Model Robust Designs". Design and Analysis of Experiments. Handbook of Statistics. pp. 1055– 1099. Cheng, C.-S. "Optimal Design: Exact Theory". Design and Analysis of Experiments. Handbook of Statistics. pp. 977– 1006.
Let X 1 be dosage "level" and X 2 be the blocking factor furnace run. Then the experiment can be described as follows: k = 2 factors (1 primary factor X 1 and 1 blocking factor X 2) L 1 = 4 levels of factor X 1 L 2 = 3 levels of factor X 2 n = 1 replication per cell N = L 1 * L 2 = 4 * 3 = 12 runs. Before randomization, the design trials look like:
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]
In probability theory, an experiment or trial (see below) is any procedure that can be infinitely repeated and has a well-defined set of possible outcomes, known as the sample space. [1] An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one.
The mathematics of gambling is a collection of probability applications encountered in games of chance and can get included in game theory.From a mathematical point of view, the games of chance are experiments generating various types of aleatory events, and it is possible to calculate by using the properties of probability on a finite space of possibilities.
(1) The Type I bias equations 1.1 and 1.2 are not affected by the sample size n. (2) Eq(1.4) is a re-arrangement of the second term in Eq(1.3). (3) The Type II bias and the variance and standard deviation all decrease with increasing sample size, and they also decrease, for a given sample size, when x's standard deviation σ becomes small ...
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of possible outcomes for an experiment. [1] [2] It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). [3]