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normal distribution

  A theoretical frequency distribution whose identifying characteristic is its bell-shaped symmetry around the three measures of its central tendency — mean, median and mode (see figure). As with all theoretical distributions, it has a smooth shape based on a histogram for an infinitely large population of values. Using the two major measures of its form (its mean and standard deviation — sd) it is possible to identify the exact location of an individual value within it — i.e. how far that value is from the mean in sd units.

Many of the test statistics used in confirmatory data analysis have normal distributions, which allow precise statements of the probability of an observed value being obtained from a random allocation procedure (e.g. the probability of getting a correlation coefficient, r, of 0.67 with a random allocation of the values across that number of observations). Thus the normal distribution is central to much parametric statistical analysis.

Deviations from the normal distribution involve skewness (in which the mean and the median are not the same value) and kurtosis. A positively skewed distribution has a longer right-hand than left-hand tail, for example, with the reverse for a negatively skewed distribution: a truncated distribution lacks one of the tails (see figure). Regarding kurtosis, a platykurtic distribution is \'flatter\' than the normal (i.e. has a relatively large sd) and a leptokurtic distribution is more \'peaked\' (has a relatively small standard deviation). (RJJ)

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normal distribution

Suggested Reading Gardiner, V. and Gardiner, G. 1978: Analysis of frequency distributions. Concepts and Techniques in Modern Geography 19. Norwich: Geo Books.



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