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Kwartet Anscombe’a 09/02/2009

Posted by Mikołaj Morzy in eksploracja danych, nauka.

Francis Anscombe był angielskim statystykiem, który dużą część życia spędził na uniwersytetach Yale i Princeton. Anscombe był jednym z pionierów analizy wizualnej i często podkreślał istotność wizualizacji zbioru danych poddawanego analizie. Na potrzeby ilustracji stworzył cztery proste zbiory danych, nazwane kwartetem Anscombe’a.

anscombeCo jest takiego ciekawego w tych czterech zbiorach? Otóż wszystkie cztery mają dokładnie te same własności statystyczne:

  • średnia \overline{x_i}= 9.0
  • wariancja \sigma^2_x= 10.0
  • średnia \overline{y_i}= 7.5
  • wariancja \sigma^2_y= 3.75
  • korelacja \rho_{x,y}= 0.816
  • regresja liniowa: y = 0.5x + 3

Ten przykład dobitnie pokazuje, jak istotne jest zapoznanie się i zaprzyjaźnienie z eksplorowanymi danymi.


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