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Factorial Designs
In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable. For the vast majority of factorial experiments, each factor has only two levels. For example, with two factors each taking two levels, a factorial experiment would have four treatment combinations in total, and is usually called a ''2×2 factorial design''. In such a design, the interaction between the variables is often the most important. This applies even to scenarios where a main effect and an interaction is present. If the number of combinations in a full factorial design ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Response Surface Metodology
Response may refer to: *Call and response (music), musical structure *Reaction (other) *Request–response **Output or response, the result of telecommunications input *Response (liturgy), a line answering a versicle *Response (music) or antiphon, a response to a psalm or other part of a religious service *Response, a phase in emergency management *Response rate (survey) Proper names and titles *''Response'', a print and online magazine of Christian thought published by Seattle Pacific University * ''Response'' (album), a studio album by Phil Wickham *Response (company), a call centre company based in Scotland * ''The Response'' (film) *The National War Memorial (Canada), titled ''The Response'' *The Northumberland Fusiliers Memorial in Newcastle upon Tyne, titled "The Response" See also *Action (other) *Answer (other) *Reply (other) *Response variable, or the realization thereof *Responsions, an examination formerly required for a degree at Ox ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wiley (publisher)
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company founded in 1807 that focuses on academic publishing and instructional materials. The company produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East Orange, New Jer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis Of Variance
Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation. In its simplest form, ANOVA provides a statistical test of whether two or more population means are equal, and therefore generalizes the ''t''-test beyond two means. In other words, the ANOVA is used to test the difference between two or more means. History While the analysis of variance reached fruition in the 20th century, antecedents extend centuries into the past according to Stigler. These include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was performing hypothesis testing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer Publishing
Springer Publishing Company is an American publishing company of academic journals and books, focusing on the fields of nursing, gerontology, psychology, social work, counseling, public health, and rehabilitation (neuropsychology). It was established in 1951 by Bernhard Springer, a great-grandson of Julius Springer, and is based in Midtown Manhattan, New York City. History Springer Publishing Company was founded in 1950 by Bernhard Springer, the Berlin-born great-grandson of Julius Springer, who founded Springer-Verlag (now Springer Science+Business Media). Springer Publishing's first landmark publications included ''Livestock Health Encyclopedia'' by R. Seiden and the 1952 ''Handbook of Cardiology for Nurses''. The company's books soon branched into other fields, including medicine and psychology. Nursing publications grew rapidly in number, as Modell's ''Drugs in Current Use'', a small annual paperback, sold over 150,000 copies over several editions. Solomon Garb's ''Labor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Orthogonality (mathematics)
In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity'' to the linear algebra of bilinear forms. Two elements ''u'' and ''v'' of a vector space with bilinear form ''B'' are orthogonal when . Depending on the bilinear form, the vector space may contain nonzero self-orthogonal vectors. In the case of function spaces, families of orthogonal functions are used to form a basis. The concept has been used in the context of orthogonal functions, orthogonal polynomials, and combinatorics. Definitions * In geometry, two Euclidean vectors are orthogonal if they are perpendicular, ''i.e.'', they form a right angle. * Two vectors, ''x'' and ''y'', in an inner product space, ''V'', are ''orthogonal'' if their inner product \langle x, y \rangle is zero. This relationship is denoted x \perp y. *An orthogonal matrix is a matrix whose column vectors are orthonormal to each other. * Two vector subspaces, ''A'' and ''B'', of an inner product spa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Biased Sample
In statistics, sampling bias is a bias in which a sample is collected in such a way that some members of the intended population have a lower or higher sampling probability than others. It results in a biased sample of a population (or non-human factors) in which all individuals, or instances, were not equally likely to have been selected. If this is not accounted for, results can be erroneously attributed to the phenomenon under study rather than to the method of sampling. Medical sources sometimes refer to sampling bias as ascertainment bias. Ascertainment bias has basically the same definition, but is still sometimes classified as a separate type of bias. Distinction from selection bias Sampling bias is usually classified as a subtype of selection bias, sometimes specifically termed sample selection bias, but some classify it as a separate type of bias. A distinction, albeit not universally accepted, of sampling bias is that it undermines the external validity of a test (the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractional Factorial Designs
In statistics, fractional factorial designs are experimental designs consisting of a carefully chosen subset (fraction) of the experimental runs of a full factorial design. The subset is chosen so as to exploit the sparsity-of-effects principle to expose information about the most important features of the problem studied, while using a fraction of the effort of a full factorial design in terms of experimental runs and resources. In other words, it makes use of the fact that many experiments in full factorial design are often redundant, giving little or no new information about the system. Notation Fractional designs are expressed using the notation ''l''k − p, where ''l'' is the number of levels of each factor investigated, ''k'' is the number of factors investigated, and ''p'' describes the size of the fraction of the full factorial used. Formally, ''p'' is the number of ''generators'', assignments as to which effects or interactions are ''confounded'', ''i.e.'', c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sparsity-of-effects Principle
In the statistical analysis of the results from factorial experiments, the sparsity-of-effects principle states that a system is usually dominated by main effects and low-order interactions. Thus it is most likely that main (single factor) effects and two-factor interactions are the most significant responses in a factorial experiment. In other words, higher order interactions such as three-factor interactions are very rare. This is sometimes referred to as the ''hierarchical ordering principle''. The sparsity-of-effects principle actually refers to the idea that only a few effects in a factorial experiment will be statistically significant. This principle is only valid on the assumption of a factor space far from a stationary point. See also * Occam's Razor * Pareto principle The Pareto principle states that for many outcomes, roughly 80% of consequences come from 20% of causes (the "vital few"). Other names for this principle are the 80/20 rule, the law of the vital few, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reproducibility
Reproducibility, also known as replicability and repeatability, is a major principle underpinning the scientific method. For the findings of a study to be reproducible means that results obtained by an experiment or an observational study or in a statistical analysis of a data set should be achieved again with a high degree of reliability when the study is replicated. There are different kinds of replication but typically replication studies involve different researchers using the same methodology. Only after one or several such successful replications should a result be recognized as scientific knowledge. With a narrower scope, ''reproducibility'' has been introduced in computational sciences: Any results should be documented by making all data and code available in such a way that the computations can be executed again with identical results. In recent decades, there has been a rising concern that many published scientific results fail the test of reproducibility, evoking a r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Experimental Error
Observational error (or measurement error) is the difference between a measured value of a quantity and its true value.Dodge, Y. (2003) ''The Oxford Dictionary of Statistical Terms'', OUP. In statistics, an error is not necessarily a " mistake". Variability is an inherent part of the results of measurements and of the measurement process. Measurement errors can be divided into two components: ''random'' and ''systematic''. Random errors are errors in measurement that lead to measurable values being inconsistent when repeated measurements of a constant attribute or quantity are taken. Systematic errors are errors that are not determined by chance but are introduced by repeatable processes inherent to the system. Systematic error may also refer to an error with a non-zero mean, the effect of which is not reduced when observations are averaged. Measurement errors can be summarized in terms of accuracy and precision. Measurement error should not be confused with measurement uncer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Product
In mathematics, specifically set theory, the Cartesian product of two sets ''A'' and ''B'', denoted ''A''×''B'', is the set of all ordered pairs where ''a'' is in ''A'' and ''b'' is in ''B''. In terms of set-builder notation, that is : A\times B = \. A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product is taken, the cells of the table contain ordered pairs of the form . One can similarly define the Cartesian product of ''n'' sets, also known as an ''n''-fold Cartesian product, which can be represented by an ''n''-dimensional array, where each element is an ''n''-tuple. An ordered pair is a 2-tuple or couple. More generally still, one can define the Cartesian product of an indexed family of sets. The Cartesian product is named after René Descartes, whose formulation of analytic geometry gave rise to the concept, which is further generalized in terms of direct product. Examples A deck of cards An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Factorial Design
In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable. For the vast majority of factorial experiments, each factor has only two levels. For example, with two factors each taking two levels, a factorial experiment would have four treatment combinations in total, and is usually called a ''2×2 factorial design''. In such a design, the interaction between the variables is often the most important. This applies even to scenarios where a main effect and an interaction is present. If the number of combinations in a full factorial design i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
