# How Minitab adds center points to a two-level factorial design

Adding center points to a two-level factorial design can let you detect curvature in the fitted data. If there is curvature that involves the center of the design, the average response at the center point is either higher or lower than the average response of all of the factorial (corner) points.

The way Minitab adds center points to the design depends on whether you have text, numeric, or a combination of text and numeric factors. Here is how Minitab adds center points:
• When all factors are numeric and the design:
• does not have blocks, Minitab adds the specified number of center points to the design.
• has blocks, Minitab adds the specified number of center points to each block.
• When all the factors in a design are text, you cannot add center points.
• When you have a combination of numeric and text factors, there is no true center to the design. In this case, center points are called pseudo-center points. When the design:
• does not have blocks, Minitab adds the specified number of center points for each combination of the levels of the text factors. In total, for Q text factors, Minitab adds 2Q times as many center points.
• has blocks, Minitab adds the specified number of center points for each combination of the levels of the text factors to each block. In each block, for Q text factors, Minitab adds 2Q times as many center points.
For example, consider a 23 design with blocks. Factors A and C are numeric with levels 0, 10 and .2, .3, respectively. Factor B is text identifying whether a catalyst exists or not. If you specify 3 center points in the Designs sub-dialog box, Minitab adds a total of 2 x 3 = 6 pseudo-center points, three points for the low level of factor B and three for the high level. These six points are:
Factor A Factor B Factor C
5 present .25
5 present .25
5 present .25
5 absent .25
5 absent .25
5 absent .25

Then, consider a 25 design with blocks where three factors are text, and there are two blocks. There are 2 x 2 x 2 = 8 combinations of text levels. If you specify two center points per block, Minitab will add 8 x 2 = 16 pseudo-center points to each of the two blocks.

###### Note

Center points are not available with split-plot designs.