Question

In a recent study, 166 adults from the st. louis area were recruited and randomly assigned to receive one of two treatments for a sinus infection. half of the subjects received an antibiotic (amoxicillin) and the other half received a placebo.

(a) describe how the researchers could have assigned treatments to subjects if they wanted to use a completely randomized design.
(b) all the subjects in the experiment had moderate, severe, or very severe symptoms at the beginning of the study. describe one statistical benefit and one statistical drawback for using subjects with moderate, severe, or very severe symptoms instead of just using subjects with very severe symptoms.
(c) at different stages during the next month, all subjects took the sino-nasal outcome test. after 10 days, the difference in average test scores was not statistically significant. in this context, explain what it means for the difference to be not statistically significant.
(d) one possible way that researchers could have improved the study is to use a randomized block design. explain how the researchers could have incorporated blocking in their design.

Answer 1

To use a completely randomized design, the researchers could randomly assign treatments to subjects. Using subjects with different symptom severities in the experiment has the benefit of increasing generalizability but may increase data variability. When the difference in test scores is not statistically significant, it means the observed difference could have occurred by chance. Blocking can be used to group subjects with a relevant characteristic before assigning treatments.

Step-by-step explanation:

(a) To use a completely randomized design for assigning treatments to subjects, the researchers could randomly assign each subject to either the antibiotic or placebo group. This can be done using a random number generator or drawing names from a hat, ensuring that each subject has an equal chance of being assigned to either group.

(b) One statistical benefit of using subjects with moderate, severe, or very severe symptoms is that it increases the generalizability of the results. It allows the researchers to study the effects of the treatments on a wider range of symptom severities. One statistical drawback is that it may increase the variability in the data, making it more challenging to detect significant differences between the treatment groups.

(c) When the difference in average test scores after 10 days is not statistically significant, it means that the observed difference could have occurred by chance alone. In other words, there is insufficient evidence to conclude that the treatments have a significant effect on the sino-nasal outcome test scores.

(d) To incorporate blocking in their design, the researchers could group the subjects based on a relevant characteristic, such as the severity of symptoms, and then randomly assign each group to the antibiotic or placebo group. This ensures that each treatment group has an equal proportion of subjects with different levels of symptom severity, reducing the potential confounding effect of symptom severity on the treatment outcomes.