The graphical process most frequently used in the analysis of data from a two-by-two crossover design. For each of the subject the difference between the response variable values on each treatment are plotted against the sum of the two treatment standards. The two groups corresponding to the order in which the treatments were given are differentiated on the plot by the different plotting symbols. A huge shift between the groups in the horizontal direction signifies a differential carryover effect. If this shift is small enough, then the shift between the groups in the vertical direction is a measure of the treatment effect. An instance of this type of plot can be seen in the figure drawn below.

 


The Higher-order differences are defined by the repeated application. So, for instance, the second difference,

 

 Often used in applications to achieve the stationarity prior to fitting models.