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The value q s is the sample's test statistic. (The notation | x | means the absolute value of x; the magnitude of x with the sign set to +, regardless of the original sign of x.) This q s test statistic can then be compared to a q value for the chosen significance level α from a table of the studentized range distribution.
Next, the upper control limit (UCL) and lower control limit (LCL) for the individual values (or upper and lower natural process limits) are calculated by adding or subtracting 2.66 times the average moving range to the process average: = ¯ + ¯.
The two plastic limit theorems apply to any elastic-perfectly plastic body or assemblage of bodies. Lower limit theorem: If an equilibrium distribution of stress can be found which balances the applied load and nowhere violates the yield criterion, the body (or bodies) will not fail, or will be just at the point of failure.
Compact Letter Display (CLD) is a statistical method to clarify the output of multiple hypothesis testing when using the ANOVA and Tukey's range tests. CLD can also be applied following the Duncan's new multiple range test (which is similar to Tukey's range test).
In general, the upper and lower approximations are not equal; in such cases, we say that target set is undefinable or roughly definable on attribute set . When the upper and lower approximations are equal (i.e., the boundary is empty), P ¯ X = P _ X {\displaystyle {\overline {P}}X={\underline {P}}X} , then the target set X {\displaystyle X} is ...
13934 and other numbers x such that x ≥ 13934 would be an upper bound for S. The set S = {42} has 42 as both an upper bound and a lower bound; all other numbers are either an upper bound or a lower bound for that S. Every subset of the natural numbers has a lower bound since the natural numbers have a least element (0 or 1, depending on ...
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Its statistical distribution is the studentized range distribution, which is used for multiple comparison procedures, such as the single step procedure Tukey's range test, the Newman–Keuls method, and the Duncan's step down procedure, and establishing confidence intervals that are still valid after data snooping has occurred. [4]