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E
ERROR TYPES
See : ALPHA, BETA, TYPE-1 ERROR, TYPE-2 ERROR.
EQUIVALENT TEST STATISTIC
Within a RANDOMISATION SET, it is possible that two different STATISTICs may be inter-related in a manner which is provably monotonic irrespective of the data. In such a situation a RANDOMISATION TEST performed on either of these TEST STATISTICs will necessarily have the same outcome in terms of ALPHA. If one of the STATISTICs is of good descriptive validity whereas the other is simpler to compute, then a RANDOMISATION TEST upon the simpler STATISTIC may be used in place of a test upon the descriptively more valid one, with corresponding savings in amount of computation required. An example of such EQUIVALENT TEST STATISTICs occurs for the situation of comparison of levels of a single INTERVAL-SCALE variable between two groups. In this situation, the descriptively valid statistic, as defined for the PITMAN PERMUTATION TEST(1), is the difference of means, but simpler EQUIVALENT TEST STATISTICS include the mean for one designated group, or (most simply) the total of scores in one designated group.
EXACT BINOMIAL TEST
A STATISTICAL TEST referring to the BINOMIAL DISTRIBUTION in its exact algebraic form, rather than through continuous approximations which are used especially where sample sizes are substantial. Also see EXACT TEST(1).
EXACT-STATS
This is the name of the academic initiative which produced this present glossary. EXACT-STATS is a closed e-mail based discussion group for the development and promulgation of the ideas of re-randomisation statistics. The contact address is : exact-stats@mailbase.ac.uk .
EXACT TEST(1)
The characteristic of a RE-RANDOMISATION TEST based upon EXHAUSTIVE RE-RANDOMISATION, that the value of ALPHA will be fixed irrespective of any random sampling of RANDOMISATIONS or upon any distributional assumptions. Notable examples are the EXACT BINOMIAL TEST, FISHER TEST(1), the PITMAN PERMUTATION TESTs(1 and 2), and various NON-PARAMETRIC TESTs based upon RANKED DATA.
EXACT TEST(2)
A test which yields an ALPHA value which does not depend upon the NOMINAL ALPHA CRITERION VALUE which may have been set for ALPHA. This is in contrast to the possible practice of producing only a yes/no decision with regard to a NOMINAL ALPHA CRITERION VALUE. Note that this reference to exactness is not (sic) the concern of the EXACT-STATS initiative.
EXHAUSTIVE RE-RANDOMISATION
A series of samples from a RANDOMISATION SET which is known to generate every RANDOMISATION. In particular, sampling which generates every RANDOMISATION exactly once.
EXPERIMENTAL DESIGN
This term overtly refers to the planning of a process of data collection. The term is also used to refer to the information necessary to describe the interrelationships within a set of data. Such a description involves considerations such as number of cases, sampling methods, identification of variables and their scale-types, identification of repeated measures and replications. These considerations are essential to guide the choice of TEST STATISTIC and the process of RE-RANDOMISATION. Also see : DEGREES OF FREEDOM, REPEATED MEASURES, REPLICATIONS, STRATIFIED, TWO-WAY TABLE.
EXTENDED PASCAL
See : PASCAL.
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