Graphs in Statistical Analysis

One of the seminal papers establishing the importance of data visualization (as it is now called) was the 1973 paper by F J Anscombe in http://www.sjsu.edu/faculty/gerstman/StatPrimer/anscombe1973.pdf

It has probably the most elegant introduction to an advanced statistical analysis paper that I have ever seen-

1. Usefulness of graphs

Most textbooks on statistical methods, and most statistical computer programs, pay too little attention to graphs. Few of us escape being indoctrinated with these notions:

(1) numerical calculations are exact, but graphs are rough;

(2) for any particular kind of statistical data there is just one set of calculations constituting a correct statistical analysis;

(3) performing intricate calculations is virtuous, whereas actually looking at the data is cheating.

A computer should make both calculations and graphs. Both sorts of output should be studied; each will contribute to understanding.

Of course the dataset makes it very very interesting for people who dont like graphical analysis too much.

From http://en.wikipedia.org/wiki/Anscombe%27s_quartet

 The x values are the same for the first three datasets.

Anscombe’s Quartet
I II III IV
x y x y x y x y
10.0 8.04 10.0 9.14 10.0 7.46 8.0 6.58
8.0 6.95 8.0 8.14 8.0 6.77 8.0 5.76
13.0 7.58 13.0 8.74 13.0 12.74 8.0 7.71
9.0 8.81 9.0 8.77 9.0 7.11 8.0 8.84
11.0 8.33 11.0 9.26 11.0 7.81 8.0 8.47
14.0 9.96 14.0 8.10 14.0 8.84 8.0 7.04
6.0 7.24 6.0 6.13 6.0 6.08 8.0 5.25
4.0 4.26 4.0 3.10 4.0 5.39 19.0 12.50
12.0 10.84 12.0 9.13 12.0 8.15 8.0 5.56
7.0 4.82 7.0 7.26 7.0 6.42 8.0 7.91
5.0 5.68 5.0 4.74 5.0 5.73 8.0 6.89

For all four datasets:

Property Value
Mean of x in each case 9 exact
Variance of x in each case 11 exact
Mean of y in each case 7.50 (to 2 decimal places)
Variance of y in each case 4.122 or 4.127 (to 3 d.p.)
Correlation between x and y in each case 0.816 (to 3 d.p.)
Linear regression line in each case y = 3.00 + 0.500x (to 2 d.p. and 3 d.p. resp.)
But see the graphical analysis –
While R has always been great in emphasizing graphical analysis, thanks in part due to work by H Wickham and others, SAS products and  language has also modified its approach at http://www.sas.com/technologies/analytics/statistics/datadiscovery/
 SAS Visual Data Discovery combines top-selling SAS products (Base SASSAS/STAT® and SAS/GRAPH®), along with two interfaces (SAS® Enterprise Guide® for guided tasks and batch analysis and JMP® software for discovery and exploratory analysis).
 and  ODS Statistical Graphs at
While ODS Statistical graphs is still not as smooth as say R’s GGPLOT2 http://tinyurl.com/ggplot2-book, it still is a progressive step
Pretty graphs make for better decisions too !

 

 

Author: Ajay Ohri

http://about.me/ajayohri

One thought on “Graphs in Statistical Analysis”

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