1.
Design of experiments
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The design of experiments is the design of any task that aims to describe or explain the variation of information under conditions that are hypothesized to reflect the variation. In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, the change in the predictor is generally hypothesized to result in a change in the second variable, hence called the outcome variable. Main concerns in design include the establishment of validity, reliability. Related concerns include achieving appropriate levels of power and sensitivity. Correctly designed experiments advance knowledge in the natural and social sciences, other applications include marketing and policy making. In 1747, while serving as surgeon on HMS Salisbury, James Lind carried out a clinical trial to compare remedies for scurvy. This systematic clinical trial constitutes a type of DOE, Lind selected 12 men from the ship, all suffering from scurvy. Lind limited his subjects to men who were as similar as I could have them and he divided them into six pairs, giving each pair different supplements to their basic diet for two weeks. The treatments were all remedies that had proposed, A quart of cider every day. Twenty five gutts of vitriol three times a day upon an empty stomach, one half-pint of seawater every day. A mixture of garlic, mustard, and horseradish in a lump the size of a nutmeg, two spoonfuls of vinegar three times a day. Two oranges and one every day. The citrus treatment stopped after six days when they ran out of fruit, apart from that, only group one showed some effect of its treatment. The remainder of the crew served as a control. Charles S. Peirce randomly assigned volunteers to a blinded, repeated-measures design to evaluate their ability to discriminate weights, peirces experiment inspired other researchers in psychology and education, which developed a research tradition of randomized experiments in laboratories and specialized textbooks in the 1800s. Charles S. Peirce also contributed the first English-language publication on a design for regression models in 1876. A pioneering optimal design for regression was suggested by Gergonne in 1815. In 1918 Kirstine Smith published optimal designs for polynomials of degree six, herman Chernoff wrote an overview of optimal sequential designs, while adaptive designs have been surveyed by S. Zacks

2.
Analysis of variance
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In the ANOVA setting, 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 or not the means of groups are equal. Hy, ANOVAs are useful for comparing three or more means for statistical significance and it is conceptually similar to multiple two-sample t-tests, but is more conservative and is therefore suited to a wide range of practical problems. While the analysis of variance reached fruition in the 20th century and these include hypothesis testing, the partitioning of sums of squares, experimental techniques and the additive model. Laplace was performing hypothesis testing in the 1770s, the development of least-squares methods by Laplace and Gauss circa 1800 provided an improved method of combining observations. It also initiated much study of the contributions to sums of squares, Laplace soon knew how to estimate a variance from a residual sum of squares. By 1827 Laplace was using least squares methods to address ANOVA problems regarding measurements of atmospheric tides, before 1800 astronomers had isolated observational errors resulting from reaction times and had developed methods of reducing the errors. An eloquent non-mathematical explanation of the effects model was available in 1885. Ronald Fisher introduced the term variance and proposed its formal analysis in a 1918 article The Correlation Between Relatives on the Supposition of Mendelian Inheritance and his first application of the analysis of variance was published in 1921. Analysis of variance became widely known after being included in Fishers 1925 book Statistical Methods for Research Workers, Randomization models were developed by several researchers. The first was published in Polish by Neyman in 1923, one of the attributes of ANOVA which ensured its early popularity was computational elegance. The structure of the model allows solution for the additive coefficients by simple algebra rather than by matrix calculations. In the era of mechanical calculators this simplicity was critical, the determination of statistical significance also required access to tables of the F function which were supplied by early statistics texts. The analysis of variance can be used as an tool to explain observations. A dog show provides an example, a dog show is not a random sampling of the breed, it is typically limited to dogs that are adult, pure-bred, and exemplary. A histogram of dog weights from a show might plausibly be rather complex, suppose we wanted to predict the weight of a dog based on a certain set of characteristics of each dog. Before we could do that, we would need to explain the distribution of weights by dividing the dog population into groups based on those characteristics. A successful grouping will split dogs such that each group has a low variance of dog weights, in the illustrations to the right, each group is identified as X1, X2, etc

3.
Between-group design
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In the design of experiments, a between-group design is an experiment that has two or more groups of subjects each being tested by a different testing factor simultaneously. This design is used in place of, or in some cases in conjunction with, the within-subject design. In order to avoid bias, experimental blinds are usually applied in between-group designs. The most commonly used type is the blind, which keeps the subjects blind without identifying them as members of the treatment group or the control group. In a single-blind experiment, a placebo is usually offered to the group members. Occasionally, the blind, a more secure way to avoid bias from both the subjects and the testers, is implemented. In this case, both the subjects and the testers are unaware of which group belong to. The double blind design can protect the experiment from the observer-expectancy effect, the utilization of the between-group experimental design has several advantages. First, multiple variables, or multiple levels of a variable, can be tested simultaneously, and with enough testing subjects, thus, the inquiry is broadened and extended beyond the effect of one variable. Additionally, this design saves a great deal of time, which is if the results aid in a time-sensitive issue. The main disadvantage with between-group designs is that they can be complex and often require a number of participants to generate any useful. For example, researchers testing the effectiveness of a treatment for severe depression might need two groups of twenty patients for a control and a test group, if they wanted to add another treatment to the research, they would need another group of twenty patients. The potential scale of these experiments can make between-group designs impractical due to limited resources, subjects, another major concern for between-group designs is bias. Assignment bias, observer-expectancy and subject-expectancy biases are common causes for skewed data results in between-group experiments, some other disadvantages for between-group designs are generalization, individual variability and environmental factors. Whilst it is easy to try to select subjects of the age, gender and background. At the same time, the lack of homogeneity within a group due to individual variability may also produce unreliable results and obscure genuine patterns, environmental variables can also influence results and usually arise from poor research design. A practice effect is the change resulting from repeated testing. Some research has been done regarding whether it is possible to design an experiment that combines within-subject design and between-group design, a way to design psychological experiments using both designs exists and is sometimes known as mixed factorial design