In 1695 about 11,400 doctors who had treated plague sufferers died and about 23,670 doctors who had not treated plague sufferers died. On the basis of these figures, it can be concluded that it was more dangerous for doctors not to participate in the treatment of plague sufferers than it was for them to participate in it. Which of the following statements would cast most doubt on the conclusion above?
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Examining the death rates for doctors in the years before and after 1695.
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Separating deaths due to natural causes during the treatment of plague suffers from deaths caused by other causes.
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Comparing death rates per thousand members of each group rather than comparing total numbers of deaths.
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The figures quoted may vary by plus or minus ten percent from the actual figures.
To solve the question, let's analyze each statement and determine which one casts the most doubt on the conclusion:
A. Examining the death rates for doctors in the years before and after 1695.
This statement would provide additional information about the death rates of doctors in different time periods, which could help determine if the death rates during 1695 were significantly different or not. If the death rates were similar in other years, it would suggest that the deaths in 1695 may not be directly related to treating plague sufferers. Therefore, this statement could cast doubt on the conclusion.
B. Separating deaths due to natural causes during the treatment of plague sufferers from deaths caused by other causes.
This statement suggests that deaths during the treatment of plague sufferers could be caused by factors unrelated to the treatment itself. By isolating deaths caused by other factors, it would help determine if treating plague sufferers directly contributed to the higher death rates among doctors. This statement provides valuable information but doesn't directly cast doubt on the conclusion.
C. Comparing death rates per thousand members of each group rather than comparing total numbers of deaths.
This statement suggests comparing death rates per thousand members of each group, which would give a more accurate representation of the risk involved. It could reveal that the death rates among doctors who treated plague sufferers were relatively higher compared to their overall population, indicating a higher risk. Conversely, it could also show that the death rates among doctors who didn't treat plague sufferers were relatively higher compared to their population, casting doubt on the conclusion. Therefore, this statement could potentially cast doubt on the conclusion.
D. The figures quoted may vary by plus or minus ten percent from the actual figures.
This statement implies a margin of error in the figures provided. While it's important to consider the accuracy of the data, it doesn't directly challenge the conclusion based on the given figures. It might affect the precision of the conclusion, but it doesn't provide contradictory information.
Therefore, based on the analysis above, the statement that would cast the most doubt on the conclusion is:
C. Comparing death rates per thousand members of each group rather than comparing total numbers of deaths.
Correct answer: Comparing death rates per thousand members of each group rather than comparing total numbers of deaths.
The argument compares raw death counts (11,400 vs 23,670) to conclude it was riskier not to treat plague patients. But this ignores the relative sizes of the two doctor groups — if there were, say, three times as many doctors who didn't treat plague patients as who did, a higher raw death count among non-treaters could still reflect a lower death rate. Without knowing group sizes, the raw totals tell us nothing about relative danger. Converting to a rate (deaths per 1,000 doctors in each group) is exactly what's needed to properly compare risk, so pointing out this omission most directly undermines the conclusion.
The other options (pre/post-1695 trends, cause-of-death breakdown, or a ±10% margin of error) don't address the core flaw of comparing absolute counts across differently-sized groups.