Normal Distribution
nothing is called 95% until it has been counted
Concept

Anscombe quartet — where it appears

Four eleven-point datasets agreeing on mean, variance, correlation, slope and intercept to two decimals while being four different shapes. Two of their four defects are not properties of the joint distribution at all, so no summary of the dependence could separate them.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Four datasets, slope 0.50, R² 0.67. Every one of these fits reports the same slope to two decimals and the same R². Only the first is a linear relationship with noise: the second is a curve, the third is a line with one outlier, and the fourth has its slope set by a single point.

Four datasets, one summary

Four datasets agree on slope, intercept and R² to two decimals. One is a linear relationship, one is a curve, one is a line with an outlier, and one has its slope set by a single point. The summary cannot tell them apart and neither can any other summary.

regression · Summary How far apart four summaries put the quartet. Each bar is the largest value minus the smallest across the four datasets. Pearson spans 0.0018, which is the construction working. Distance correlation — the measure that is zero if and only if the variables are independent — spans 0.101, and Spearman spans 0.491.

The summary that was meant to work

Distance correlation is zero if and only if two variables are independent, which is exactly the guarantee a correlation coefficient lacks. Run on the four datasets that share a correlation, it spreads them by 0.10 — and Spearman, which guarantees nothing, spreads them by 0.49.

spread · Summary

Named alongside it

The objects these essays reach for when they reach for this one.

LeverageModel diagnosticsResidual plotSummary statisticsCorrelationDistance correlationRank correlation

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