Estimation
estimation, in statistics, any of numerous procedures used to calculate the value of some property of a population from observations of a sample drawn from the population. A point estimate, for example, is the single number most likely to express the value of the property.
An interval estimate defines a range within which the value of the property can be expected degree of confidence) to fall. The 18th-century English theologian and mathematician Thomas Bayes was instrumental in the development of Bayesian estimation to facilitate revision of estimates on the basis of further information. In sequential estimation the experimenter evaluates the precision of the estimate during the sampling process, which is terminated as soon as the desired degree of precision has been achieved.
distribution function
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distribution function
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Alternate titles: cumulative distribution function, probability distribution
distribution function, mathematical expression that describes the probability that a system will take on a specific value or set of values. The classic examples are associated with games of chance. The binomial distribution gives the probabilities that heads will come up a times and tails n − a times when a fair coin is tossed n times. Many phenomena, such as the distribution of approximate the classic bell-shaped, or normal, curve (see normal distribution).
The highest point on the curve indicates the most common or modal value, which in most cases will be close to the average (mean) for the population. A well-known example from physics is the Maxwell-Boltzmann distribution law, which specifies the probability that a molecule of gas will be found with velocity components u, v, and w in the x, y, and z directions. A distribution function may take into account as many variables as one chooses to include.
distribution function, mathematical expression that describes the probability that a system will take on a specific value or set of values. The classic examples are associated with games of chance. The binomial distribution gives the probabilities that heads will come up a times and tails times when a fair coin is tossed n times. Many phenomena, such as the distribution of approximate the classic bell-shaped, or normal.
The highest point on the curve indicates the most common or modal value, which in most cases will be close to the average for the population. A well-known example from physics is the Maxwell-Boltzmann distribution law, which specifies the probability that a molecule of gas will be found with velocity components u, v, and w in the x, y, and z directions. A distribution function may take into account as many variables as one chooses to include.
correlation
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correlation, In statistics, the degree of association between two random variables. The correlation between the graphs of two data sets is the degree to which they resemble each other. However, correlation is not the same as causation, and even a very close correlation may be no more than a coincidence. Mathematically, a correlation is expressed by a correlation coefficient that ranges.
Related Topics: degree of freedom probability sampling producer’s risk non probability sampling acceptance sampling.
sampling, in statistics, a process or method of drawing a representative group of individuals or cases from a particular population. Sampling and statistical inference are used in circumstances in which it is impractical to obtain information from every member of the population, as in biological or chemical analysis, industrial quality control, or social surveys. The basic sampling design is simple random sampling, based on probability theory. In this form of random sampling, every element of the population being sampled has an equal probability of being selected. In a random sample of a class of 50 students, for example, each student has the same probability, 1/50, of being selected.
Every combination of elements drawn from the population also has an equal probability of being selected. Sampling based on probability theory allows the investigator to determine the likelihood that statistical findings are the result of chance. More commonly used methods, refinements of this basic idea, are stratified sampling which the population is divided into classes and simple random samples are drawn cluster sampling (in which the unit of the sample is a group, such as a household), and systematic sampling.
An alternative to probability sampling is judgment sampling, in which selection is based on the judgment of the researcher and there is an unknown probability of inclusion in the sample for any given case. Probability methods are usually preferred because they avoid selection bias and make it possible to estimate.
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