Datasaurus_dozen

Datasaurus dozen

Datasaurus dozen

Thirteen data sets with the same descriptive statistics, yet very different distributions

The Datasaurus dozen comprises thirteen data sets that have nearly identical simple descriptive statistics to two decimal places, yet have very different distributions and appear very different when graphed.[1] It was inspired by the smaller Anscombe's quartet that was created in 1973.

Data

The following table contains summary statistics for all thirteen data sets.

More information of the linear regression: ...
thirteen graphs of the datasets in the Datasaurus Dozen, visualized graphically and also summarized numerically to show their statistical summaries are similar, while their graphical representations are not similar
The thirteen data sets in the Datasaurus Dozen, visualized and summarized

The thirteen data sets were labeled as the following:

  • away
  • bullseye
  • circle
  • dino
  • dots
  • h_lines
  • high_lines
  • slant_down
  • slant_up
  • star
  • v_line
  • wide_lines
  • x_shape

Similar to the Anscombe's quartet, the Datasaurus dozen was designed to further 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 data sets.[2][3][4][5][1][6]

Creation

The dinosaur data set created by Alberto Cairo that inspired the creation of the Datasaurus Dozen

The first data set, in the shape of a Tyrannosaurus, that inspired the rest of the "datasaurus" data set was constructed in 2016 by Alberto Cairo.[7][8] It was proposed by Maarten Lambrechts that this data set also be called "Anscombosaurus".[7]

This data set was then accompanied by twelve other data sets that were created by Justin Matejka and George Fitzmaurice at Autodesk. Unlike the Anscombe's quartet, where it is not known how the data set was generated,[9] the authors used simulated annealing to make these data sets. They made small, random, and biased changes to each point towards the desired shape. Each shape took 200,000 iterations of perturbations to complete.[1]

The pseudocode for this algorithm is as follows:

current_ds ← initial_ds
for x iterations, do:
    test_ds ← perturb(current_ds, temp)
    if similar_enough(test_ds, initial_ds):
        current_ds ← test_ds

function perturb(ds, temp):
    loop:
        test ← move_random_points(ds)
        if fit(test) > fit(ds) or temp > random():
            return test

where

  • initial_ds is the seed data set
  • current_ds is the latest version of the data set
  • fit() is a function used to check whether moving the points gets closer to the desired shape
  • temp is the temperature of the simulated annealing algorithm0
  • similar_enough() is a function that checks whether the statistics for the two given data sets are similar enough
  • move_random_points() is a function that randomly moves data points

See also

References

  1. [1]
    Matejka, Justin; Fitzmaurice, George (2017-05-02). "Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated Annealing" (PDF). Proceedings of the 2017 CHI Conference on Human Factors in Computing Systems. CHI '17. New York, NY, USA: Association for Computing Machinery: 1290–1294. doi:10.1145/3025453.3025912. ISBN 978-1-4503-4655-9. Archived from the original on 2017-05-02.
  2. [2]
    Elert, Glenn (2021). "Linear Regression". The Physics Hypertextbook.
  3. [3]
    Janert, Philipp K. (2010). Data Analysis with Open Source Tools. O'Reilly Media. pp. 65–66. ISBN 978-0-596-80235-6.
  4. [4]
    Chatterjee, Samprit; Hadi, Ali S. (2006). Regression Analysis by Example. John Wiley and Sons. p. 91. ISBN 0-471-74696-7.
  5. [5]
    Saville, David J.; Wood, Graham R. (1991). Statistical Methods: The geometric approach. Springer. p. 418. ISBN 0-387-97517-9.
  6. [6]
    Tufte, Edward R. (2001). The Visual Display of Quantitative Information (2nd ed.). Cheshire, CT: Graphics Press. ISBN 0-9613921-4-2.
  7. [7]
    Cairo, Alberto. "Download the Datasaurus: Never trust summary statistics alone; always visualize your data". Retrieved 2024-02-01.
  8. [8]
    Murtagh, Jack (2024-02-01). "What This Graph of a Dinosaur Can Teach Us about Doing Better Science". Scientific American. Retrieved 2024-03-08.
  9. [9]
    Chatterjee, Sangit; Firat, Aykut (2007). "Generating Data with Identical Statistics but Dissimilar Graphics: A follow up to the Anscombe dataset". The American Statistician. 61 (3): 248–254. doi:10.1198/000313007X220057. JSTOR 27643902. S2CID 121163371.
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