9.1.1: Datasaurus Dozen
- Page ID
- 60371
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The Datasaurus Dozen: Why We Always Plot Our Data
Up to this point, we've talked about plotting two quantitative variables to find direction or pattern. But you might ask: "Do I really have to make a scatterplot if I already have the means, standard deviations, and correlation?"
Yes. And here's why.
The Datasaurus Dozen is a group of datasets created by Justin Matejka and George Fitzmaurice in 2017 as an update to Anscombe’s classic 1973 datasets. These twelve different datasets all have roughly the same:
- Mean of x
- Mean of y
- Standard deviations
- Correlation between x and y
But when we look at scatterplots of the data, the patterns and stories are completely different.
Shared Descriptive Statistics
| Dataset | Mean of x | Mean of y | Standard Deviation of x | Standard Deviation of y | Correlation (r) |
|---|---|---|---|---|---|
| Dino (Original) | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
| Star | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
| X-Shape | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
| H-Shape | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
| Circle | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
| Slant-Up | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
| Slant-Down | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
| Vertical Lines | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
| Horizontal Lines | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
| Tight Cluster | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
| Wide Spread | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
| Target Shape | 54.26 | 47.83 | 16.77 | 26.94 | –0.06 |
Plots of all the data
By IngmundForberg - Own work, CC BY-SA 4.0, Link
Why This Matters
If you only look at summary statistics, you might assume that all of these distributions are the same but they’re radically different when visualized.
This teaches us something vital: summary statistics don’t tell the full story. We must always plot our data to detect patterns, outliers, structures, or shapes that numbers alone might hide.
This is especially important as we move into correlation where we'll quantify how strong a linear relationship is. But beware: even strong-looking numbers can mislead if we don’t first look at our data with our own eyes.