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Anscombe 1973: the quartet, four data sets with the same summary statistics

ToolData Summary and Outliers
SourceAnscombe, F. J. (1973). "Graphs in Statistical Analysis." The American Statistician, Vol. 27, No. 1, pp. 17–21.
LevelUndergraduate

Problem

Anscombe's four x, y data sets of eleven points each share the same means, variances and regression line although their scatter plots differ completely. Compute the summary statistics and the correlation of each pair.

Inputs to Enter

  • Columns x1, y1, x2, y2, x3, y3, x4, y4 of the quartet (x1 = x2 = x3 = 10, 8, 13, 9, 11, 14, 6, 4, 12, 7, 5; x4 = 8 except one 19)
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Answers

  • Means 9 and 7.50 in every set; Pearson r = 0.816 for every pair; regression line y = 3 + 0.5 x
  • The Spearman correlations differ between the sets (scipy values in the test script)

Notes

Paste the eight columns with a header line; the correlation matrix section gives Pearson and Spearman for every pair.

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