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R
RANDOM SAMPLE
A SAMPLE drawn from a POPULATION in such a way that every individual of the POPULATION has an equal chance of appearing in the SAMPLE. This ensures that the SAMPLE is REPRESENTATIVE, and provides the necessary basis for virtually all forms of inference from SAMPLE to POPULATION, including the informal inference which is characteristic of RE-RANDOMISATION statistics. PSEUDO-RANDOM procedures can be useful in defining a RANDOM SAMPLE.
RANDOMISATION(1)
Generation of whole or part of the RANDOMISATION SET. Also see : RANDOMISATION(3), RE-RANDOMISATION.
RANDOMISATION(2)
The process of arranging for data-collection, in accordance with the EXPERIMENTAL DESIGN, such that there should be no foreseeable possibilty of any systematic relationship between the data and any measureable characteristic of the procedure by which the data was sampled. This is usually arranged by assigning experimental units to groups, and REPEATED MEASURES to experimental units, on a strictly random basis.
RANDOMISATION(3)
One of the arrangements making up the RANDOMISATION SET. These arranegments will be encountered in the act of RANDOMISATION(1). Also see : BRANCH AND BOUND, MINIMAL-CHANGE SEQUENCE.
RANDOMISATION DISTRIBUTION
A collection of values of the TEST STATISTIC obtained by undertaking a number of RE-RANDOMISATIONS of the actual data within the RANDOMISATION SET. ALso see : CONFIDENCE INTERVAL, RANDOMISATION TEST.
RANDOMISATION SET
The collection of possible RE-RANDOMISATIONs of data within the constraints of the EXPERIMENTAL DESIGN. Also see : RANDOMISATION DISTRIBUTION.
RANDOMISATION TEST
The rationale of a RANDOMISATION TEST involves exploring RE-RANDOMISATIONs of the actual data to form the RANDOMISATION DISTRIBUTION of values of the TEST STATISTIC. The OUTCOME VALUE value of the TEST STATISTIC is judged in terms of its relative position within the RE-RANDOMISATION DISTRIBUTION. If the OUTCOME VALUE is near to one extreme of the RE-RANDOMISATION DISTRIBUTION then it may be judged that it is in the extreme TAIL of the distribution, with reference to a NOMINAL ALPHA CRITERION VALUE, and thus judged to show STATISTICAL SIGNIFICANCE. Also see : EXACT TEST(1).
RANKED DATA
This refers to the practice of taking a set of N data, to be regarded as ORDINAL-SCALE, amd replacing each datum by its rank (1 .. N) within the set. Also see : WILCOXON RANK-SUM TEST.
RATIO SCALE
This is a type of MEASUREMENT SCALE for which it is meaningful to reason in terms of differences in scores (see INTERVAL SCALE) and also in terms of ratios of scores. Such a scale will have a zero point which is meaningful in the sense that it indicates complete absence of the property which the scale measures. The RATIO SCALE may be either unipolar (negative values not meaningful) or bipolar (both positive and negative values meaningful), and either continuous or discrete.
RE-RANDOMISATION
The process of generating alternative arrangements of given data which would be consistent with the EXPERIMENTAL DESIGN. Also see : BOOTSTRAP, EXACT TEST(2), EXHAUSTIVE RE-RANDOMISATION, MONTE-CARLO, RE-RANDOMISATION STATISTICS.
RE-RANDOMISATION STATISTICS
Also known as PERMUTATION or RANDOMISATION(1) statistics. These are the specific area of concern of this present glossary.
RELATIVE POWER
A comparison of two or more statistical tests, for the same EXPERIMENTAL DESIGN, SAMPLE SIZE, and NOMINAL ALPHA CRITERION VALUE, in terms of the respective values of POWER. Also see : BETA.
REPEATED-MEASURES
This is a feature of an EXPERIMENTAL DESIGN whereby several observations measured on a common scale refer to the same sampling unit. Identification of the relation of the individual observations to the EXPERIMENTAL DESIGN is crucial to this definition. Examples : the measurement of water level at a particular site on several systematically-defined occasions; measurement of reaction-time of an individual using right hand and left hand separately. Also see : INDEPENDENT GROUPS, REPLICATIONS, STRATIFIED.
REPLICATIONS
This is a feature of an EXPERIMENTAL DESIGN whereby observations on an experimental unit are repeated under the same conditions. Identification of the position of a particular observation within the sequence of replications is irrelevant. Also see : REPEATED MEASURES, STRATIFIED.
REPRESENTATIVE
Patterns in a SAMPLE of units may reasonably be attributed to the POPULATION from which the SAMPLE is drawn, only if the SAMPLE is REPRESENTATIVE. In practical terms, to ensure that a SAMPLE is REPRESENTATIVE almost always means ensuring that it is a RANDOM SAMPLE.
RESAMPLING STATS
This is the name of an educational initiative involving the use of a PROGRAMMING LANGUAGE, in the form of an INTERPRETER, allowing the user to specify MONTE-CARLO RESAMPLING of a set of data and accumulation of the RANDOMISATION DISTRIBUTION of a defined TEST STATISTIC.
RNG
Acronym for Random Number Generator. This is a process which uses a arithmetic algorithm to generate sequences of PSEUDO-RANDOM numbers. Also see : SEED.
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