Use the following data to answer the next five exercises: A pair of studies was performed to measure the effectiveness of a new software program designed to help stroke patients regain their problem-solving skills. Patients were asked to use the software program twice a day, once in the morning and once in the evening. The studies observed $200$stroke patients recovering over a period of several weeks. The first study collected the data in Table 1.31. The second study collected the data in Table 1.32.

Patients who used the software were also a part of an exercise program whereas patients who did not use the software were not. Does this change the validity of the conclusions from Exercise 1.31?

A pair of studies were conducted to assess the efficacy of a new software program designed to assist stroke patients in regaining problem-solving skills. The software program was to be used twice a day, once in the morning and once in the evening, by the patients. The studies followed the recovery of $200$stroke patients over a period of several weeks. The data in Table 1.31 were gathered in the first study. Table 1.32 contains the results of the second study.

If the study includes two independent factors: exercise program and software use, and then the observations are made, the statistical observations will be interpreted very differently. We would not conclude that the software is significantly effective in improving things on its own. The exercise program may also contribute to the improvement. As a result, the validity of the first study's conclusions is compromised.