Anscombe’s quartet

Take, for example, Anscombe s Quartet data set shown in Figure 20." Here, there are four sets of 11 pairs of XY data which when subjected to the standard linear regression approach all yield identical numerical outputs. Cursory inspection of the numerical listing does not reveal the information immediately apparent when simply plotting the XY data (Figure 21). The Chinese proverb that a picture is worth ten thousand words is amply illustrated. 

Many examples might be given to demonstrate that the use of the correlation coefficient alone is not a good option to decide about the linear straight line behaviour of our calibrators. But a very nice and well-known example should suffice. This was presented by statistician Francis Anscombe in 1973," and it is known as the Anscombe s quartet . It consists of four datasets almost identical in their average properties but definitely different in their acceptability (by analytical chemists) and overall behaviour (see Table 2.2). 

Table 2.2 Anscombe s quartet series of standardization data.

Figure 2.3 Residuals for series II of Anscombe s quartet plotted versus the order in which the standards were measured.

---