Two groups of students are conducting the same experiment on some sample units. There are two factors which can be adjusted to affect the outcome. Each factor has only two settings. There are only two students in each group. Group 1 does their experiment in the following way: every treatment is only applied to one unit, then both students read the measurements and record their readings. Group 2 does their experiment in another way: each treatment is applied to two units, and each student reads only one of the measurements. The two groups have the same number of observations. What are the differences between their observations? In what situation would one group obtain more accurate results than the other? Why? Is there a block factor?
Suppose in Problem 2, the settings of the two factors require highly accurate measurements. Minor deviation from the nominal value of the settings could lead to the failure of the experiment, which is judged by the reading of the outcome. If the measurement is less than a certain value, this run of the experiment fails. The following table shows how Group 2 conducts the experiment. For example, in the first run, setting of the two factors is completed by student A and the measurement is read by the same student. Note that in this table, each treatment has been applied to two units.
| Run | Factor One | Factor Two | Setting | Reading |
| 1 | + | + | A | A |
| 2 | + | + | A | A |
| 3 | + | - | A | A |
| 4 | + | - | B | B |
| 5 | - | + | B | B |
| 6 | - | + | A | A |
| 7 | - | - | A | A |
| 8 | - | - | B | B |
The higher the reading, the better is the experimental run. If the reading shows that this run fails, it has to be repeated again by the same student. Is there any problem with this design? What suggestion can you provide to improve the design?