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Difficulty: MediumPercentages vs. Numbers Flaws

Public Health Official: Ten years ago, asthma cases represented 8%8\% of all respiratory-related emergency room visits in our county. Last year, asthma cases represented 18%18\% of all respiratory-related emergency room visits. Clearly, a greater number of people in our county are suffering from severe asthma attacks requiring emergency care than a decade ago.

Which of the following most accurately describes a flaw in the public health official's reasoning?

  1. treats an increase in the percentage of a whole as definitive evidence of an increase in the absolute number of items in that categoryAnswer
  2. B
    infers a causal connection between the passage of time and an increase in respiratory emergencies based merely on a statistical correlation
  3. C
    incorrectly assumes that a statistical trend observed within a specific category of medical visits applies equally to all types of emergency room visits
  4. D
    draws a sweeping conclusion about most asthma patients based on statistics that apply only to some of those patients
  5. E
    fails to distinguish between the main conclusion regarding the number of asthma attacks and a subsidiary premise concerning respiratory-related emergency room visits

Answer

The correct answer is the option stating that the argument treats an increase in the percentage of a whole as definitive evidence of an increase in the absolute number of items in that category.
The official's argument concludes that the absolute number of asthma cases has increased simply because asthma now makes up a larger percentage of a specific group (respiratory ER visits). This is logically flawed because it ignores changes to the total size of that group. If the total number of respiratory-related emergency room visits plummeted over the last decade, 18%18\% of the new, smaller total could represent a smaller absolute number of patients than 8%8\% of the old, much larger total.

Step-by-Step Solution

1
Analyze the premises provided in the stimulus.
The premise states that the percentage of respiratory-related ER visits attributed to asthma increased from 8%8\% to 18%18\% over a decade.
To establish the factual basis the official is using for their argument.
2
Identify the conclusion drawn by the official.
The official concludes that the absolute number of asthma cases requiring emergency care has increased.
To determine exactly what the argument is trying to prove.
3
Evaluate the logical gap between the premises and the conclusion.
The premises provide information exclusively about proportions (percentages of a specific category), but the conclusion makes a definitive claim about absolute numbers (a greater number of people).
To locate the structural flaw in the reasoning.
4
Determine what information is missing that makes the conclusion invalid.
The argument ignores the overall size of the baseline group (total respiratory ER visits). If total respiratory ER visits dropped dramatically, 18%18\% of the new, smaller total could be fewer actual patients than 8%8\% of the old, larger total.
To precisely define the percentage vs. number fallacy occurring in the stimulus.

Key Concept

Percentages vs. Numbers Flaws
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Topics

Percentages vs. Numbers Flaws

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