Question

In an experiment, 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. 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. Explain what it means that this difference was not statistically significant.

a. The difference in the average test scores for the two groups was small enough that it is unlikely to be explained by chance variation in the random assignment to treatments.
b. The difference in the average test scores for the two groups was large enough that it is unlikely to be explained by chance variation in the random assignment to treatments.
c. The difference in the average test scores for the two groups was small enough that it could be explained by chance variation in the random assignment to treatments.
d. The difference in the average test scores for the two groups was large enough that it could be explained by chance variation in the random assignment to treatments.

Answer 1

The lack of statistical significance in the test scores between the two treatment groups suggests that the observed difference could be due to random chance rather than the effectiveness of the medication.

Step-by-step explanation:

When we say the difference in average test scores was not statistically significant, it means that the observed difference could be due to random chance, and not necessarily due to the effectiveness of the medication. Given this scenario, answer choice c is correct: The difference in the average test scores for the two groups was small enough that it could be explained by chance variation in the random assignment to treatments.

The goal of the statistical analysis in such experiments is to determine whether the results represent a true effect or if they're likely the result of random variation. If the results were statistically significant, we would conclude that the treatment had an actual impact. But in this case, because the results are not statistically significant, there is insufficient evidence to say that the antibiotic treatment for a sinus infection is more effective than the placebo.