Anscombe's quartet

There is a very interesting dataset illustrating how careful we must be when only using summary statistics and correlation coefficients to describe our data. It also shows us that plotting is not optional. Anscombe's quartet is a collection of four different datasets that have identical summary statistics and correlation coefficients, but when plotted, it is obvious they are not similar. Each dataset consists of eleven (x,y) points. They were constructed in 1973 by the statistician Francis Anscombe to demonstrate both the importance of graphing data when analyzing it, and the effect of outliers and other influential observations on statistical properties. He described the article as being intended to counter the impression among statisticians that "numerical calculations are exact, but graphs are rough."

Notice that each of the plots in Figure shown above has an identical best-fit line defined by the equation y = 0.50x + 3.00. In the next section, we will discuss, at a high level, how this line is created and what it means.

The quartet is still often used to 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 datasets. 

Summary statistics are very helpful when we're getting to know the data, but be wary of relying exclusively on them. Remember, statistics can be misleading; be sure to also plot the data before drawing any conclusions or proceeding with the analysis.

In the next post we will learn about prediction and forecasting using regression