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In statistics, efficiency is a measure of quality of an estimator, of an experimental design, [1] or of a hypothesis testing procedure. [2] Essentially, a more efficient estimator needs fewer input data or observations than a less efficient one to achieve the Cramér–Rao bound.
It is known that the least squares estimator minimizes the variance of mean-unbiased estimators (under the conditions of the Gauss–Markov theorem). In the estimation theory for statistical models with one real parameter , the reciprocal of the variance of an ( "efficient" ) estimator is called the " Fisher information " for that estimator. [ 7 ]
For example, an experimental uncertainty analysis of an undergraduate physics lab experiment in which a pendulum can estimate the value of the local gravitational acceleration constant g. The relevant equation [ 1 ] for an idealized simple pendulum is, approximately,
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle.
Cohen's kappa measures the agreement between two raters who each classify N items into C mutually exclusive categories. The definition of is =, where p o is the relative observed agreement among raters, and p e is the hypothetical probability of chance agreement, using the observed data to calculate the probabilities of each observer randomly selecting each category.
Constraints may involve institutional review boards, informed consent and confidentiality affecting both clinical (medical) trials and behavioral and social science experiments. [42] In the field of toxicology, for example, experimentation is performed on laboratory animals with the goal of defining safe exposure limits for humans . [ 43 ]
This equation is similar to the equation involving (,) in the introduction (this is the matrix version of that equation). When X and e are uncorrelated , under certain regularity conditions the second term has an expected value conditional on X of zero and converges to zero in the limit, so the estimator is unbiased and consistent.
The Rüchardt experiment, [1] [2] [3] invented by Eduard Rüchardt, is a famous experiment in thermodynamics, which determines the ratio of the molar heat capacities of a gas, i.e. the ratio of (heat capacity at constant pressure) and (heat capacity at constant volume) and is denoted by (gamma, for ideal gas) or (kappa, isentropic exponent, for real gas).