Match each of the following logical arguments to the abstract description that most accurately identifies its specific statistical reasoning flaw.
- The city transit authority reports that the number of traffic accidents involving bicycles has doubled over the past five years. Therefore, cycling in the city has become significantly more dangerous for the average cyclist.Infers a change in the likelihood of an event's occurrence from a change in the absolute number of such occurrences, without considering whether the total number of opportunities for the event to occur has also changed.
- Ten years ago, a much larger proportion of the national workforce was employed in manufacturing than is the case today. Thus, there must be fewer people employed in manufacturing today than there were ten years ago.Deduces a decrease in a specific absolute numerical value solely from a decline in that value's proportional representation within a larger whole.
- Over the past decade, the percentage of the university's budget allocated to scientific research has steadily increased. Therefore, the scientific research department is currently receiving more funding in actual dollars than it did a decade ago.Presumes, without providing justification, that an increase in a segment's relative share of a total guarantees an increase in the absolute size of that segment.
- Last month, 80 percent of the employees who received promotions were from the marketing department, while only 20 percent were from the engineering department. Clearly, a marketing employee is more likely to receive a promotion than an engineering employee.Infers that an outcome is disproportionately likely for members of a particular group based on that group's representation among all outcomes, without providing information about the group's representation in the general population.
Cevap
The bicycle accidents argument matches the flaw of inferring likelihood from absolute occurrences; the manufacturing workforce argument matches deducing an absolute decrease from a proportional decline; the university budget argument matches presuming an absolute increase from a relative share; and the promotions argument matches inferring likelihood from outcome representation without baseline context.
Each argument represents a distinct manifestation of the Percentages vs. Numbers flaw. The first conflates absolute increases with rate increases. The second and third conflate proportional changes with absolute changes. The fourth conflates the composition of a subset of outcomes with the comparative likelihood of those outcomes occurring for individuals within the general population.
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Anahtar Kavram
Identifying subtle variations in how arguments conflate percentages, rates, proportions, and absolute numbers.
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