Two Sources, One Claim: An ED Nurse's Post and a State Bulletin
A nursing student is writing a short paper on seasonal influenza and has collected two sources.
Source A - a public post by an emergency-department nurse with 40,000 followers: "Our ER is drowning. We've seen more flu this week than in the entire month of last December, and about half of the sickest patients told me they got the shot. Do the math. If the vaccine worked, my department would be empty."
Source B - a state health department weekly bulletin: "For the week ending January 6, lab-confirmed influenza hospitalizations rose from 42 to 118 statewide. Among hospitalized adults with known vaccination status (n = 96), 63 percent reported not receiving this season's vaccine. Vaccination status was self-reported in 40 percent of cases. Statewide vaccination coverage is estimated at 48 percent of adults."
The student must decide which claims each source can actually support before drafting. Both texts are reproduced in full; no additional statistics are available.
1. Source A says "do the math." Identify the reasoning error in that instruction and name the information that would be required to make the comparison valid.
Read the worked answer
The error: missing denominators (base-rate neglect). Source A compares a count of vaccinated patients against an unstated total and treats "half of the sickest got the shot" as proof the vaccine fails. That comparison is meaningless without knowing what share of the surrounding population is vaccinated.
What is needed:
- The vaccination rate in the population the ER draws from.
- The total number of flu patients seen, not just "the sickest" the nurse happened to speak with.
- A stated method for how vaccination status was obtained.
Why it matters, concretely: Source B supplies the relevant rate - 48 percent of adults vaccinated. If roughly half the population is vaccinated and 37 percent of hospitalized patients with known status were vaccinated, that is not evidence of failure; it is close to what partial protection looks like in a heavily vaccinated group. The arithmetic only has force once the vaccinated share of the population is entered.
Second error: "the sickest patients told me" is selection by anecdote. The nurse remembers the memorable cases.
2. Which source is more reliable for a claim about statewide influenza trends, and which specific features of the texts drive that judgment?
Read the worked answer
Source B is more reliable for that claim - but the judgment has to be made feature by feature, not by institutional reputation alone.
Features favoring B:
- Counts with a defined window and a stated trend (42 to 118, week ending January 6), which can be checked and compared.
- Disclosed limitations: the bulletin itself reports that vaccination status was self-reported in 40 percent of cases and that the denominator is 96, not 118. A source that names its own weak points is more usable than one that does not.
- Purpose is to report, not to persuade; no rhetorical imperative like "do the math."
Features of A: A is a firsthand observation and may be a legitimate signal that a unit is strained - that part is credible. But its purpose is advocacy, its evidence is recalled conversation, and it generalizes from one department to a statewide claim.
Key distinction: A may be accurate about workload and still unable to support a claim about vaccine effectiveness. Judging a source means matching its evidence to the specific claim, not rating it globally.
3. How does the phrase "with known vaccination status (n = 96)" limit what the bulletin's 63 percent figure can be used to say?
Read the worked answer
The limit: 63 percent is not a percentage of all 118 hospitalized patients. It describes only the 96 whose status was known. The remaining 22 are outside the calculation entirely, and the bulletin does not say which direction they would push the number.
The second, compounding limit: of the cases that are counted, 40 percent had self-reported status. Self-report is subject to recall error and to social desirability - a patient may misremember or may say what seems expected. So even the 96 is not a cleanly measured group.
Correct phrasing: "Among hospitalized adults whose vaccination status was known, 63 percent reported not receiving this season's vaccine."
Incorrect phrasing to reject: "63 percent of hospitalized flu patients were unvaccinated." That sentence silently deletes both the 22 unknowns and the self-report caveat.
Why this matters as a reading skill: the qualifier sits in the same sentence as the number, and skipping it is the most common way a careful-looking citation becomes a misstatement. Precision here is a comprehension question, not a statistics question.