The treatments of a 2 in the power of 2 factorial design can be represented by using a square. In this case, let’s make the horizontal line be the substrate. Then we have at the left side the treatments with the substrate that low level and that the right side, the treatments with the substrate at high level; and the vertical line be the enzyme, then in the bottom of the square, we have the low level of the enzyme and at the top of the square, the high level of enzyme. We can represent the treatments of a 2 in the power of k factorial design by lower case letters. The presence of a lower case letter means that the factor is being tested at its high level and the absence of a lower case letter means that the factor is being tested at its low level.
In our case, when we have substrate that high level, an enzyme at low level, we have treatment a. When we have substrate that low level and enzyme at high level, we have treatment b. When we have both of them at high level, we have the treatment ab, and if both of them are at the low level, we call the treatment (1). The symbols (1), a, b and ab also represents the total or the sum of all the responses of n replicates of each treatment.
Now going back to the table with the experiments, we are going to add a column with the treatments. Then the first one, both of them at low level, treatment one. The second, A at high-level, treatment a; the third, B at high-level, treatment b, and finally substrate an enzyme at high-level, treatment ab. And now we add the column with the total or sum of each treatment. Treatment (1), a, b, and ab. Finally, we're going to add the information about the sum to the square representation.