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Spurious correlation is a term coined by Karl Pearson to describe the correlation between ratios of absolute measurements that arises as a consequence of using ratios, rather than because of any actual correlations between the measurements. The phenomenon of spurious correlation is one of the main motives for the field of compositional data analysis which deals with the analysis of variables that carry only relative information, such as proportions, percentages and parts-per-million. Pearson's definition of spurious correlation is distinct from misconceptions about correlation and causality, or the term spurious relationship. ==Illustration of spurious correlation== Pearson states a simple example of spurious correlation:〔 The upper scatter plot on the right illustrates this example using 500 observations of ''x'', ''y'', and ''z''. Variables ''x'', ''y'' and ''z'' are drawn from normal distributions with means 10, 10, and 30, respectively, and standard deviations 1, 1, and 3 respectively, i.e., : Even though ''x'', ''y'', and ''z'' are statistically independent (i.e., pairwise uncorrelated), the ratios x/z and y/z have a sample correlation of 0.53. This is because of the common divisor (''z'') and can be better understood if we colour the points in the scatter plot by the ''z''-value. Trios of (''x'', ''y'', ''z'') with relatively large ''z'' values tend to appear in the bottom left of the plot; trios with relatively small ''z'' values tend to appear in the top right. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Spurious correlation」の詳細全文を読む スポンサード リンク
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