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significance test

  A statistical procedure for identifying the probability of an observed event having occurred by chance. Most statistics, such as chi square and the correlation coefficient (r), have an associated sampling distribution of possible values with its own mean and standard error (the latter is equivalent to the standard deviation of a frequency distribution). For example, a 3 × 3 matrix will have a large number of possible sets of cell values for a given set of row and column totals, each of which will produce a different value of chi square when compared with the observed distribution (see also entropy-maximizing models). Because the frequency distribution of chi square is known for every table size (i.e. numbers of rows and columns, the product of which — less one in each case — is the degrees of freedom for the test), then the probability of getting an observed value can be obtained readily from the relevant statistical table.

Significance tests are used in two ways. In confirmatory data analysis they assist the testing of hypotheses about the characteristics of a population, undertaken through a study of a properly selected sample (see sampling). For example, a chi-square test may be conducted to see if the age structure of two counties varies (i.e. if they are both samples of the same population). If, according to the frequency distribution, the observed value of chi square would occur very frequently for samples of that size, given the degrees of freedom, it is concluded that the two counties do not differ significantly. The usual criterion for \'very frequently\' is more than one test in 20 (normally stated as at the 95 per cent or 0.05 level). If the observed value occurs only rarely in the frequency distribution, then it is unlikely that the observed value has occurred by chance and it is concluded that the difference between the two samples is almost certainly present in the population from which they were drawn (i.e. the two county populations combined).

In exploratory data analysis the significance test is not used to draw a conclusion about a population from a sample (see inference) but rather to indicate the likely importance of an observed result. Again, the comparison is with what would happen if the only influences were random; if the observed value of the statistic falls in one of the tails (the extreme values) of the theoretical frequency distribution it is concluded that what has been observed is so unlikely to have occurred by chance that it must be \'real\' and worthy of further investigation. (RJJ)

Suggested Reading O\'Brien, L. 1992: Introducing quantitative geography: measurement, methods and generalised linear models. London and New York: Routledge. Hay, A.M. 1985: Statistical tests in the absence of sample: a note. Professional Geographer 37: 334-8.



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