[Named as one of a developmental sequence of theoretical programming languages : 'A', 'B' (also the useful language BCPL)]. A PROGRAMMING LANGUAGE of broad expressive power; thus suitable for both numerical and general programming. 'C' is closely associated with the construction of the ubiquitous computer operating system 'unix'. COMPILERS for 'C' are supplied for virtually all modern computers. 'C' is available as a STANDARD PROGRAMMING LANGUAGE approved by ANSI and ISO.
Where expected frequencies are sufficiently high, hypothesised distributions of counts may be approximated by a NORMAL DISTRIBUTION rather than an exact BINOMIAL DISTRIBUTION. The corresponding distribution of the CHI-SQUARED STATISTIC can be derived algebraically - this is the CHI-SQUARED DISTRIBUTION which has been computed and published historically as extensive printed tables. Use of the tables is notably simple, as the CHI-SQUARED DISTRIBUTION depends upon only one parameter, the DEGREES OF FREEDOM, defined as one less than the number of categories.
[Named by E.S. Pearson ()?]. This is a long-established TEST STATISTIC for measuring the extent to which a set of categorical outcomes depart from a hypothesised set of probabilities. It is calculated as a sum of terms over the available categories, where each term is of the form : ((O-E)^2)/E ; 'O' represents the observed frequency for the category and 'E' represents the corresponding expected frequency based upon multiplying the sample size by the hypothesised probability for the category being considered (therefore 'E' will generally not be an integer value). In situations where the number of categories is 2 an alternative procedure is to use an EXACT BINIOMIAL TEST. Also see : CHI-SQUARED DISTRIBUTION, MULTINOMIAL DISTRIBUTION, POISSON PROCESS.
A PROGRAM supplied especially for a particular type of COMPUTER, to enable the translation of code expressed in some PROGRAMMING LANGUAGE into OBJECT CODE for that COMPUTER. A COMPILER undertakes translation of the whole of the user's PROGRAM to produce an OBJECT CODE version which is complete, undivided and potentially permanent; this is in contrast to the action of an INTERPRETER.
An automatic data-processing device which is PROGRAMMABLE. Also see : COMPUTER PROGRAM, OBJECT CODE, PROGRAM.
A specification of how to undertake a certain process, usually expressed via a PROGRAMMING LANGUAGE, for some chosen COMPUTER. Also see : PROGRAM.
For a given RE-RANDOMISATION distribution, a family of related distributions may be defined according to a range of hypothetical values of the pattern which the TEST STATISTIC measures. For instance, for the PITMAN PERMUTATION TEST(2) to test for a scale shift between two groups, a related distribution may be formed by shifting all the observations in one group by a common amount, where this common shift is regarded as a continuous variable. With finite numbers of data the number of related distributions will be finite, and typically considerably smaller than the number of points of the RANDOMISATION DISTRIBUTION. The likelihood of the OUTCOME VALUE may be calculated for each distribution in the family, and these likelihoods may be then used to define a contiguous set of values which occupy a certain proportion of the total unit weight of the likelihoods integrated over all values of the TEST STATISTIC. The CONFIDENCE INTERVAL is defined by the minimum and maximum values of the range of values so defined. The proportion of the total weight within the range of values is regarded as an ALPHA probability that the value of the TEST STATISTIC lies within this range. Generally the definition of a CONFIDENCE INTERVAL cannot be unique without imposing further constraints. Approaches to providing suitable constraints, such that a CONFIDENCE INTERVAL will be unique, include defining the CONFIDENCE INTERVAL : to include the whole of one TAIL of the distribution; or to be centred in some sense upon the OUTCOME VALUE; or to be centred between TAILS of equal weight. In the case of RE-RANDOMISATION DISTRIBUTIONs, these are DISCRETE DISTRIBUTIONS so there will generally be no range of values with weight corresponding exactly to an arbitrary NOMINAL ALPHA CRITERION LEVEL, and the problem of non-uniqueness is therefore not generally solvable.
A probability distribution of a continuous STATISTIC, based upon an algebraic formula, such that for any possible value of the cumulative probability there is an exact corresponding value of the STATISTIC in question. Also see : DISCRETE DISTRIBUTION.