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Generalized Randomized Block Design
In randomized statistical experiments, generalized randomized block designs (GRBDs) are used to study the interaction between blocks and treatments. For a GRBD, each treatment is replicated at least two times in each block; this replication allows the estimation and testing of an interaction term in the linear model (without making parametric assumptions about a normal distribution for the error). Univariate response GRBDs versus RCBDs: Replication and interaction Like a randomized complete block design (RCBD), a GRBD is randomized. Within each block, treatments are randomly assigned to experimental units: this randomization is also independent between blocks. In a (classic) RCBD, however, there is no replication of treatments within blocks. Two-way linear model: Blocks and treatments The experimental design guides the formulation of an appropriate linear model. Without replication, the (classic) RCBD has a two-way linear-model with treatment- and block-effects but ''withou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomized Experiment
In science, randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects. Randomization-based inference is especially important in experimental design and in survey sampling. Overview In the statistical theory of design of experiments, randomization involves randomly allocating the experimental units across the treatment groups. For example, if an experiment compares a new drug against a standard drug, then the patients should be allocated to either the new drug or to the standard drug control using randomization. Randomized experimentation is ''not'' haphazard. Randomization reduces bias by equalising other factors that have not been explicitly accounted for in the experimental design (according to the law of large numbers). Randomization also produces ignorable designs, which are valuable in model-based statistical inference, especially Bayesian or likelihood-based. In the design of experiments, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multivariate Analysis
Multivariate statistics is a subdivision of statistics encompassing the simultaneous observation and analysis of more than one outcome variable. Multivariate statistics concerns understanding the different aims and background of each of the different forms of multivariate analysis, and how they relate to each other. The practical application of multivariate statistics to a particular problem may involve several types of univariate and multivariate analyses in order to understand the relationships between variables and their relevance to the problem being studied. In addition, multivariate statistics is concerned with multivariate probability distributions, in terms of both :*how these can be used to represent the distributions of observed data; :*how they can be used as part of statistical inference, particularly where several different quantities are of interest to the same analysis. Certain types of problems involving multivariate data, for example simple linear regression an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomized Experiment
In science, randomized experiments are the experiments that allow the greatest reliability and validity of statistical estimates of treatment effects. Randomization-based inference is especially important in experimental design and in survey sampling. Overview In the statistical theory of design of experiments, randomization involves randomly allocating the experimental units across the treatment groups. For example, if an experiment compares a new drug against a standard drug, then the patients should be allocated to either the new drug or to the standard drug control using randomization. Randomized experimentation is ''not'' haphazard. Randomization reduces bias by equalising other factors that have not been explicitly accounted for in the experimental design (according to the law of large numbers). Randomization also produces ignorable designs, which are valuable in model-based statistical inference, especially Bayesian or likelihood-based. In the design of experiments, th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Randomization
Randomization is the process of making something random. Randomization is not haphazard; instead, a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern, but follow an evolution described by probability distributions. For example, a random sample of individuals from a population refers to a sample where every individual has a known probability of being sampled. This would be contrasted with nonprobability sampling where arbitrary individuals are selected. In various contexts, randomization may involve: * generating a random permutation of a sequence (such as when shuffling cards); * selecting a random sample of a population (important in statistical sampling); * allocating experimental units via random assignment to a treatment or control condition; * generating random numbers (random number generation); or * transforming a data stream (such as when using a scrambler in telecommunications). Applications Randomi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Interaction (statistics)
In statistics, an interaction may arise when considering the relationship among three or more variables, and describes a situation in which the effect of one causal variable on an outcome depends on the state of a second causal variable (that is, when effects of the two causes are not additive). Although commonly thought of in terms of causal relationships, the concept of an interaction can also describe non-causal associations (then also called moderation or effect modification). Interactions are often considered in the context of regression analyses or factorial experiments. The presence of interactions can have important implications for the interpretation of statistical models. If two variables of interest interact, the relationship between each of the interacting variables and a third "dependent variable" depends on the value of the other interacting variable. In practice, this makes it more difficult to predict the consequences of changing the value of a variable, particu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incomplete Block Design
In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as ''blocks'', chosen such that frequency of the elements satisfies certain conditions making the collection of blocks exhibit symmetry (balance). They have applications in many areas, including experimental design, finite geometry, physical chemistry, software testing, cryptography, and algebraic geometry. Without further specifications the term ''block design'' usually refers to a balanced incomplete block design (BIBD), specifically (and also synonymously) a 2-design, which has been the most intensely studied type historically due to its application in the design of experiments. Its generalization is known as a t-design. Overview A design is said to be ''balanced'' (up to ''t'') if all ''t''-subsets of the original set occur in equally many (i.e., ''λ'') blocks. When ''t'' is unspecified, it can usually be assumed to be 2, which means that ea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Complete Block Design
In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another. Blocking can be used to tackle the problem of pseudoreplication. Use Blocking reduces unexplained variability. Its principle lies in the fact that variability which cannot be overcome (e.g. needing two batches of raw material to produce 1 container of a chemical) is confounded or aliased with a(n) (higher/highest order) interaction to eliminate its influence on the end product. High order interactions are usually of the least importance (think of the fact that temperature of a reactor or the batch of raw materials is more important than the combination of the two - this is especially true when more (3, 4, ...) factors are present); thus it is preferable to confound this variability with the higher interaction. Examples *Male and Female: An experiment is designed to test a new drug on patients. There are two levels of the treat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blocking (statistics)
In the statistical theory of the design of experiments, blocking is the arranging of experimental units in groups (blocks) that are similar to one another. Blocking can be used to tackle the problem of pseudoreplication. Use Blocking reduces unexplained variability. Its principle lies in the fact that variability which cannot be overcome (e.g. needing two batches of raw material to produce 1 container of a chemical) is confounded or aliased with a(n) (higher/highest order) interaction to eliminate its influence on the end product. High order interactions are usually of the least importance (think of the fact that temperature of a reactor or the batch of raw materials is more important than the combination of the two - this is especially true when more (3, 4, ...) factors are present); thus it is preferable to confound this variability with the higher interaction. Examples *Male and Female: An experiment is designed to test a new drug on patients. There are two levels of the trea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Block Design
In combinatorial mathematics, a block design is an incidence structure consisting of a set together with a family of subsets known as ''blocks'', chosen such that frequency of the elements satisfies certain conditions making the collection of blocks exhibit symmetry (balance). They have applications in many areas, including experimental design, finite geometry, physical chemistry, software testing, cryptography, and algebraic geometry. Without further specifications the term ''block design'' usually refers to a balanced incomplete block design (BIBD), specifically (and also synonymously) a 2-design, which has been the most intensely studied type historically due to its application in the design of experiments. Its generalization is known as a t-design. Overview A design is said to be ''balanced'' (up to ''t'') if all ''t''-subsets of the original set occur in equally many (i.e., ''λ'') blocks. When ''t'' is unspecified, it can usually be assumed to be 2, which means that ea ... [...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] |
Tukey's Test Of Additivity
In statistics, Tukey's test of additivity, named for John Tukey, is an approach used in two-way ANOVA (regression analysis involving two qualitative factors) to assess whether the factor variables ( categorical variables) are additively related to the expected value of the response variable. It can be applied when there are no replicated values in the data set, a situation in which it is impossible to directly estimate a fully general non-additive regression structure and still have information left to estimate the error variance. The test statistic proposed by Tukey has one degree of freedom under the null hypothesis, hence this is often called "Tukey's one-degree-of-freedom test." Introduction The most common setting for Tukey's test of additivity is a two-way factorial analysis of variance (ANOVA) with one observation per cell. The response variable ''Y''''ij'' is observed in a table of cells with the rows indexed by ''i'' = 1,..., ''m'' and the columns indexe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cost
In production, research, retail, and accounting, a cost is the value of money that has been used up to produce something or deliver a service, and hence is not available for use anymore. In business, the cost may be one of acquisition, in which case the amount of money expended to acquire it is counted as cost. In this case, money is the input that is gone in order to acquire the thing. This acquisition cost may be the sum of the cost of production as incurred by the original producer, and further costs of transaction as incurred by the acquirer over and above the price paid to the producer. Usually, the price also includes a mark-up for profit over the cost of production. More generalized in the field of economics, cost is a metric that is totaling up as a result of a process or as a differential for the result of a decision. Hence cost is the metric used in the standard modeling paradigm applied to economic processes. Costs (pl.) are often further described based on their t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
