Why visualize data?

Research methods classes in graduate school generally teach important skills such as probability and statistical theory, regression, analysis of variance (ANOVA), maximum likelihood estimation (MLE), etc. While these are important methods for analyzing data and assessing research questions, sometimes drawing a picture (aka visualization) can be more precise than conventional statistical computations.1

Consider the following 13 data sets. What are the corresponding relationships between \(X\) and \(Y\)? Using traditional metrics, the relationships appear identical across the samples:

ID\(N\)\(\bar{X}\)\(\bar{Y}\)\(\sigma_{X}\)\(\sigma_{Y}\)\(R\)
114254.347.816.826.9-0.064
214254.347.816.826.9-0.069
314254.347.816.826.9-0.068
414254.347.816.826.9-0.064
514254.347.816.826.9-0.060
614254.347.816.826.9-0.062
714254.347.816.826.9-0.069
814254.347.816.826.9-0.069
914254.347.816.826.9-0.069
1014254.347.816.826.9-0.063
1114254.347.816.826.9-0.069
1214254.347.816.826.9-0.067
1314254.347.816.826.9-0.066

\(X\) and \(Y\) have the same mean and standard deviation in each dataset, and the correlation coefficient (Pearson’s \(r\)) is virtually identical. If we estimated linear regression models for each dataset, we would obtain virtually identical coefficients (again suggesting the relationships are identical):

But what happens if we draw a picture?2

Remarkably each of the datasets have the same summary statistics and linear relationships, yet they are drastically different in appearance! A good picture tells the reader much more than any table or text can provide.

1 Session Info

## ─ Session info ───────────────────────────────────────────────────────────────
##  setting  value                       
##  version  R version 3.6.1 (2019-07-05)
##  os       macOS Catalina 10.15.3      
##  system   x86_64, darwin15.6.0        
##  ui       X11                         
##  language (EN)                        
##  collate  en_US.UTF-8                 
##  ctype    en_US.UTF-8                 
##  tz       America/Chicago             
##  date     2020-03-04                  
## 
## ─ Packages ───────────────────────────────────────────────────────────────────
##  package     * version date       lib source        
##  assertthat    0.2.1   2019-03-21 [1] CRAN (R 3.6.0)
##  backports     1.1.5   2019-10-02 [1] CRAN (R 3.6.0)
##  blogdown      0.17.1  2020-02-13 [1] local         
##  bookdown      0.17    2020-01-11 [1] CRAN (R 3.6.0)
##  broom       * 0.5.5   2020-02-29 [1] CRAN (R 3.6.0)
##  callr         3.4.2   2020-02-12 [1] CRAN (R 3.6.1)
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##  crayon        1.3.4   2017-09-16 [1] CRAN (R 3.6.0)
##  datasauRus  * 0.1.4   2018-09-20 [1] CRAN (R 3.6.0)
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## 
## [1] /Library/Frameworks/R.framework/Versions/3.6/Resources/library