Datasaurus dozen

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

Data

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

Property	Value	Accuracy
Number of elements	142	exact
Mean of x	54.26	to 2 decimal places
Sample variance of x: s² _x	16.76	to 2 decimal places
Mean of y	47.83	to 2 decimal places
Sample variance of y: s² _y	26.93	to 2 decimal places
Correlation between x and y	−0.06	to 3 decimal places
Linear regression line	y = 53 − 0.1x	to 0 and 1 decimal places, respectively
Coefficient of determination of the linear regression: $R^{2}$	0.004	to 3 decimal places

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 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 algorithm
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

References

^ ^a ^b ^c 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. pp. 1290–1294. doi:10.1145/3025453.3025912. ISBN 978-1-4503-4655-9. Archived from the original on 2017-05-02.
^ Elert, Glenn (2021). "Linear Regression - Practice". The Physics Hypertextbook.
^ Janert, Philipp K. (2010). Data Analysis with Open Source Tools. O'Reilly Media. pp. 65–66. ISBN 978-0-596-80235-6.
^ Chatterjee, Samprit; Hadi, Ali S. (2006). Regression Analysis by Example. John Wiley and Sons. p. 91. ISBN 0-471-74696-7.
^ Saville, David J.; Wood, Graham R. (1991). Statistical Methods: The geometric approach. Springer. p. 418. ISBN 0-387-97517-9.
^ Tufte, Edward R. (2001). The Visual Display of Quantitative Information (2nd ed.). Cheshire, CT: Graphics Press. ISBN 0-9613921-4-2.
^ ^a ^b Cairo, Alberto. "Download the Datasaurus: Never trust summary statistics alone; always visualize your data". Retrieved 2024-02-01.
^ Murtagh, Jack (2024-02-01). "What This Graph of a Dinosaur Can Teach Us about Doing Better Science". Scientific American. Retrieved 2024-03-08.
^ 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.

External links

Animated examples from Autodesk for the Datasaurus Dozen datasets
datasauRus, datasets from the Datasaurus Dozen in R
The Datasaurus Dozen in CSV and tab-delimited files https://www.openintro.org/data/index.php?data=datasaurus

[:0-1] 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. pp. 1290–1294. doi:10.1145/3025453.3025912. ISBN 978-1-4503-4655-9. Archived from the original on 2017-05-02.

[2] Elert, Glenn (2021). "Linear Regression - Practice". The Physics Hypertextbook.

[3] Janert, Philipp K. (2010). Data Analysis with Open Source Tools. O'Reilly Media. pp. 65–66. ISBN 978-0-596-80235-6.

[4] Chatterjee, Samprit; Hadi, Ali S. (2006). Regression Analysis by Example. John Wiley and Sons. p. 91. ISBN 0-471-74696-7.

[5] Saville, David J.; Wood, Graham R. (1991). Statistical Methods: The geometric approach. Springer. p. 418. ISBN 0-387-97517-9.

[6] Tufte, Edward R. (2001). The Visual Display of Quantitative Information (2nd ed.). Cheshire, CT: Graphics Press. ISBN 0-9613921-4-2.

[:1-7] Cairo, Alberto. "Download the Datasaurus: Never trust summary statistics alone; always visualize your data". Retrieved 2024-02-01.

[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.

[ChatterjeeFirat-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.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

Data

Creation

See also

References

External links