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Hospital Rooms When patients are admitted to hospitals, they are sometimes assigned to a single room with one bed and sometimes assigned to a double room, with a roommate. (Some insurance companies will pay only for the less expensive, double rooms.) A researcher was interested in the effect of the type of room on the length of stay in the hospital. Assume that we are not dealing with health issues that require single rooms. Suppose that upon admission to the hospital, the names of patients who would have been assigned a double room were put onto a list and a systematic random sample was taken; every tenth patient who would have been assigned to a double room was part of the experiment. For each participant, a coin was flipped: If it landed heads up, she or he got a double room, and if it landed tails up, a single room. Then the experimenters observed how many days the patients stayed in the hospital and compared the two groups. The experiment ran for two months. Suppose those who stayed in single rooms stayed (on average) one less day, and suppose the difference was significant. a. Can you generalize to others from this experiment? If so, to whom can you generalize, and why can you do it? b. Can you infer causality from this study? Why or why not?

Step by step solution

01

Understanding the Experiment

This was a controlled experiment where patients were randomly assigned to either a single or a double room. The purpose of the experiment was to study the effect of the type of room on patients' length of stay. After observing and running the experiment for two months, it was found that patients in single rooms, on average, stayed one less day and this difference was significant.

02

Interpretation of Results and Generalization

The experiment's result shows that patients staying in single rooms tend to leave hospitals earlier than those in double rooms. This result is significant, implying that it is not by coincidence, but likely due to the experience in a single room (more privacy, decreased possibility of infection, etc). As to generalization, since the experiment involved systematic random sampling, it allows for generalization to the wider population of patients who do not require single rooms for health issues and would have otherwise been assigned double rooms. However, this generalization cannot be applied to those requiring single rooms due to their health concerns.

03

Determination of Causality

Yes, it can be inferred that having a single room causes shorter hospital stays, to a certain extent. This is because the experiment had controlled conditions and random assignment, which mitigates confounding variables and increases the likelihood of the observed result (less hospital stay) being a direct consequence of the independent variable (rooming situation). Nevertheless, other variables not considered in this study might also contribute to the length of hospital stays, and the relationship might not be directly causal, but there's strong evidence of it from this study.

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