With central location, one of the two fundamental ways of summarising a distribution of observations on a continuous variable (or discrete variable taking numeric values). Typically given as the Standard Deviation or variance but sometimes as the Inter-Quartile Range (IQR).

The range, often as the pair of the minimum and maximum values, or as the difference between those two, is also a measure of spread, clearly of the full spread of the data, but as it’s determined only by those two values it is arguably a much less good summary statistic for spread. For example, in a large enough sample, probably all the possible scores on any item of a questionnaire will be recorded at least once for every item so every item will have the same range. However, items may differ very much in variance if one has many people scoring mainly at one end of the possible scores but another has a much wider “spread” of scores. That’s shown here for six items from the CORE-OM an real non-help-seeking sample. All six have a score range of 4 (0 to 4) but the three risk domain items on the top row have SDs from .47 to .6 whereas the three problem domain items on the bottom row have SDs from 1.12 to 1.29.

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Standard Deviation (SD)
Inter-Quartile Range (IQR)
Distribution shape

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Not particularly covered anywhere though most nearly in Chapters 5 and 8.

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Created 13/11/21.

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