Studentized range Wikipedia. In statistics, the studentized range is the difference between the largest and smallest data in a sample measured in units of sample standard deviations, so long as the standard deviation used is independent of the data. Applied Linear Statistical Models Michael H Kutner Pdf File' title='Applied Linear Statistical Models Michael H Kutner Pdf File' />The studentized range, q, is named for William Sealy Gosset who wrote under the pseudonym Student, and was introduced by him 1. The concept was later presented by a number of actual students, Newman 1. Keuls 1. 95. 2 3 and John Tukey in some unpublished notes. Tukeys range test, the NewmanKeuls method, and the Duncans step down procedure, and establishing confidence intervals that are still valid after data snooping has occurred. DescriptioneditThe value of the studentized range is most often represented by the variable q. The studentized range can be defined based on a random sample x. N0, 1 distribution of numbers, and another random variable s that is independent of all the xi, and s. The National Kidney Foundations Kidney Disease Outcomes Quality Initiative KDOQI has provided evidencebased guidelines for all stages of chronic kidney disease. In statistics, the studentized range is the difference between the largest and smallest data in a sample measured in units of sample standard deviations, so long as. In statistics and uncertainty analysis, the WelchSatterthwaite equation is used to calculate an approximation to the effective degrees of freedom of a linear. Thenqn,maxx. 1, , xnminx. Studentized range distribution for n groups and degrees of freedom. In applications, the xi are typically the means of samples each of size m, s. The critical value of q is based on three factors the probability of rejecting a true null hypothesisn the number of observations or groups the degrees of freedom used to estimate the sample varianceDistribution normal data and applicationseditIf X1,., Xn are independent identically distributedrandom variables that are normally distributed, the probability distribution of their studentized range is what is usually called the studentized range distribution. Applied Linear Statistical Models Michael H Kutner Pdf File' title='Applied Linear Statistical Models Michael H Kutner Pdf File' />Note that the definition of q does not depend on the expected value or the standard deviation of the distribution from which the sample is drawn, and therefore its probability distribution is the same regardless of those parameters. The Studentized range distribution has applications to hypothesis testing and multiple comparisons procedures. For example, Tukeys range test and Duncans new multiple range test MRT, in which the sample x. When only the equality of the two groups means is in question i. Paulo 49074 So 46318 do 40723 Brasil 38043 da 37922 Da 35214 US 33367 Folha 2900 Local 19724 Reportagem 1790 Jos 15364. Students t distribution, differing only in that the first takes into account the number of means under consideration, and the critical value is adjusted accordingly. The more means under consideration, the larger the critical value is. This makes sense since the more means there are, the greater the probability that at least some differences between pairs of means will be significantly large due to chance alone. Studentized dataeditGenerally, the term studentized means that the variables scale was adjusted by dividing by an estimate of a population standard deviation see also studentized residual. The fact that the standard deviation is a sample standard deviation rather than the populationstandard deviation, and thus something that differs from one random sample to the next, is essential to the definition and the distribution of the Studentized data. The variability in the value of the samplestandard deviation contributes additional uncertainty into the values calculated. This complicates the problem of finding the probability distribution of any statistic that is studentized. Windows Xp Professional 64 Bit Download Iso Deutschland. See alsoeditStudent 1. Errors of routine analysis. Biometrika. 1. 9 12 1. Newman D. 1. 93. The Distribution of Range in Samples from a Normal Population Expressed in Terms of an Independent Estimate of Standard Deviation. Biometrika. 3. 1 2. Keuls M. 1. 95. 2. The Use of the Studentized Range in Connection with an Analysis of Variance. Euphytica. 1 1. 121. John A. Rafter 2. Multiple Comparison Methods for Means. SIAM. 4. 4 2 2. Pearson Hartley 1. Section 1. 4. 2ReferenceseditPearson, E. S. Hartley, H. O. Biometrika Tables for Statisticians, Volume 1, 3rd Edition, Cambridge University Press. ISBN 0 5. 21 0. Further readingeditJohn Neter, Michael H. Kutner, Christopher J. Nachtsheim, William Wasserman 1. Applied Linear Statistical Models, fourth edition, Mc. Graw Hill, page 7. John A. Rice 1. 99. Mathematical Statistics and Data Analysis, second edition, Duxbury Press, pages 4. Douglas C. Montgomery 2. Design and Analysis of Experiments, eighth edition, Wiley, page 9.