Anscombe's quartet comprises four datasets that have nearly identical simple

descriptive statistics A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and an ...

, yet have very different distributions and appear very different when graphed. Each dataset consists of eleven (''x'', ''y'') points. They were constructed in 1973 by the

statistician A statistician is a person who works with Theory, theoretical or applied statistics. The profession exists in both the private sector, private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, a ...

Francis Anscombe to demonstrate both the importance of graphing data when analyzing it, and the effect of

outlier In statistics, an outlier is a data point that differs significantly from other observations. An outlier may be due to a variability in the measurement, an indication of novel data, or it may be the result of experimental error; the latter are ...

s and other influential observations on statistical properties. He described the article as being intended to counter the impression among statisticians that "numerical calculations are exact, but graphs are rough".

Data

For all four datasets: * The first scatter plot (top left) appears to be a simple linear relationship, corresponding to two correlated variables, where ''y'' could be modelled as gaussian with mean linearly dependent on ''x''. * For the second graph (top right), while a relationship between the two variables is obvious, it is not linear, and the

Pearson correlation coefficient In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviatio ...

is not relevant. A more general regression and the corresponding coefficient of determination would be more appropriate. * In the third graph (bottom left), the modelled relationship is linear, but should have a different regression line (a

robust regression In robust statistics, robust regression seeks to overcome some limitations of traditional regression analysis. A regression analysis models the relationship between one or more independent variables and a dependent variable. Standard types of re ...

would have been called for). The calculated regression is offset by the one

, which exerts enough influence to lower the correlation coefficient from 1 to 0.816. * Finally, the fourth graph (bottom right) shows an example when one high-leverage point is enough to produce a high correlation coefficient, even though the other data points do not indicate any relationship between the variables. The quartet is still often used to illustrate the importance of looking at a set of data graphically before starting to analyze according to a particular type of relationship, and the inadequacy of basic statistic properties for describing realistic datasets. The datasets are as follows. The ''x'' values are the same for the first three datasets.

It is not known how Anscombe created his datasets. Since its publication, several methods to generate similar datasets with identical statistics and dissimilar graphics have been developed. One of these, the '' Datasaurus dozen'', consists of points tracing out the outline of a dinosaur, plus twelve other datasets that have the same summary statistics.

References

{{Reflist

External links

Department of Physics, University of Toronto

Dynamic Applet
made in GeoGebra showing the data & statistics and also allowing the points to be dragged (Set 5).
Animated examples from Autodesk
called the "Datasaurus Dozen".

for the datasets in R. Misuse of statistics Statistical charts and diagrams Statistical data sets 1973 introductions 1973 in science Data and information visualization

Data

See also

References

External links