k > 1, the number of groups > 0, the degrees of freedom
Support
PDF
CDF
In probability and statistics, studentized range distribution is the continuous probability distribution of the studentized range of an i.i.d. sample from a normally distributed population.
Suppose that we take a sample of size n from each of k populations with the same normal distribution N(μ, σ2) and suppose that is the smallest of these sample means and is the largest of these sample means, and suppose s² is the pooled sample variance from these samples. Then the following statistic has a Studentized range distribution.
and 20 Related for: Studentized range distribution information
probability and statistics, studentizedrangedistribution is the continuous probability distribution of the studentizedrange of an i.i.d. sample from a...
finding the probability distribution of any statistic that is studentized. Studentizedrangedistribution Tukey's range test Student (1927). "Errors of routine...
In statistics, a studentized residual is the dimensionless ratio resulting from the division of a residual by an estimate of its standard deviation, both...
Newman-Keuls Rodger’s Method Scheffé’s Method Tukey’s Test (see also: StudentizedRangeDistribution) Sometimes the temptation to engage in post hoc analysis is...
Q-distribution or q-distribution may refer to: Q-function, the tail distribution function of the standard normal distribution The studentizedrange distribution...
theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable...
limits of a particular taxon's distribution is its range, often represented as shaded areas on a map. Patterns of distribution change depending on the scale...
Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution f (...
with a range at and below a probability input the likelihood that a random variable is realized in that range for some probability distribution. It is...
finding the probability distribution of a Studentized statistic. In computational statistics, the idea of using Studentized statistics is of some importance...
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number...
Many probability distributions that are important in theory or applications have been given specific names. The Bernoulli distribution, which takes value...
In statistics, the Wishart distribution is a generalization of the gamma distribution to multiple dimensions. It is named in honor of John Wishart, who...
expert-elicited quantiles to smooth, continuous probability distributions. Fields of application are wide-ranging, and include economics, science, engineering, and...
of a normal distribution) in a z-score (or "standard score"), and standardize residuals in a t-statistic, or more generally studentized residuals. If...
continuous cumulative distribution function (CDF) can be used for the link since the CDF's range is [ 0 , 1 ] {\displaystyle [0,1]} , the range of the binomial...
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible...
interquartile range of a continuous distribution can be calculated by integrating the probability density function (which yields the cumulative distribution function—any...
In statistics, a sampling distribution or finite-sample distribution is the probability distribution of a given random-sample-based statistic. If an arbitrarily...
whatever the distribution of these values. Reference ranges that are given by this definition are sometimes referred as standard ranges. Since a range is a defined...
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![{\displaystyle {\begin{matrix}f_{\text{R}}(q;k,\nu )={\frac {\,{\sqrt {2\pi \,}}\,k\,(k-1)\,\nu ^{\nu /2}\,}{\Gamma (\nu /2)\,2^{\left(\nu /2-1\right)}}}\int _{0}^{\infty }s^{\nu }\,\varphi ({\sqrt {\nu \,}}\,s)\,\times \\[0.5em]\left[\int _{-\infty }^{\infty }\varphi (z+q\,s)\,\varphi (z)\,\left[\Phi (z+q\,s)-\Phi (z)\right]^{k-2}\,\mathrm {d} z\right]\,\mathrm {d} s\end{matrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a08d81086431dd9b1ebae17991b17d2ee4642b6)
![{\displaystyle {\begin{matrix}F_{\text{R}}(q;k,\nu )={\frac {\,{\sqrt {2\pi \,}}\,k\,\nu ^{\nu /2}\,}{\,\Gamma (\nu /2)\,2^{\left(\nu /2-1\right)}}}\int _{0}^{\infty }s^{\nu -1}\,\varphi ({\sqrt {\nu \,}}\,s)\,\times \\[0.5em]\qquad \left[\int _{-\infty }^{\infty }\varphi (z)\,\left[\Phi (z+q\,s)-\Phi (z)\right]^{k-1}\,\mathrm {d} z\right]\,\mathrm {d} s\end{matrix}}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/b83772014edd9847eab4060054dce9407acffaf2)
