LogicalDUAL-USE

Per Capita vs. Total

What it is

Choosing between a raw total and a rate per person — or per mile, per dose, per unit of output — according to which ranking makes the point, when the two orderings differ because the populations differ.

How it works

Big places have big totals. Worked: country A records 10,000 deaths among 300 million people, about 3 per 100,000; country B records 2,000 among 5 million, 40 per 100,000. A “has the most deaths” and B “has the highest rate”, and a presenter with a conclusion in mind picks the sentence that serves it. Neither number is wrong; they answer different questions. A hospital planner needs totals, a resident deciding whether to worry needs the rate, and a fair comparison between places needs the rate with the totals shown. The manipulation is choosing the denominator by its effect and hiding the alternative. Rates carry their own trap: a tiny population produces extreme rates from a handful of events, which is why the smallest counties top both the best and worst lists of almost any per-capita ranking, and why per-capita claims about small places should be read with the small-sample entry in mind. The unit matters too — a city's rate, a state's rate and a country's rate for the same phenomenon can order the same places three ways.

Real-world examples

  • •Chicago recorded about 800 murders in 2021, the most of any US city, and was cited on that basis by commentators on the right; its rate, around 30 per 100,000, was well below St. Louis, Baltimore and New Orleans, each above 50. Both facts were true and each side quoted one.
  • •Third Way's 2022 report “The Red State Murder Problem” ranked states by murders per capita and found the highest rates in states that voted Republican; critics replied that state rates aggregate cities governed by the other party. The unit of comparison — state or city — decided which party the statistic indicted.
  • •China emits the most carbon dioxide of any country in total, while the United States emits far more per person; in climate negotiations each country's representatives have cited the measure that assigns responsibility to the other.
  • •In 2020 the United States had the largest number of reported COVID-19 deaths in the world, a fact used by critics of the federal response, while its deaths per capita that year were below several European countries, a fact used by its defenders; both were accurate.

Ethical guidelines

Where the line is

Either the total or the rate is legitimate when the other is shown or readily available, the denominator is named and the choice follows from the question being answered; it becomes manipulation when the presenter selects the denominator for the ranking it produces, hides the alternative, or switches between units and denominators across a comparison so that each side of it is measured differently.

  • ●Give both the total and the rate, with the denominator, and say which one answers the question at hand and why.
  • ●Choose the denominator before you see the ranking, for a stated reason; if a different reasonable denominator reverses the result, report that.
  • ●Do not compare a rate for one unit (a city) with a rate for another (a state) as if they were the same measurement.
  • ●Flag rates computed from small populations, where a few events produce an extreme figure.

How to defend against it

  • ►Whenever you hear “the most” or “the highest”, ask whether it is a total or a rate, and ask for the other one.
  • ►Ask what the denominator is and whether it is the right one for the question: per person, per mile driven, per dose given, per unit of energy — the honest denominator is the exposure that produces the events.
  • ►Compare like with like: check that both sides of a comparison use the same unit (city, county, state) and the same denominator before accepting a ranking.
  • ►For per-capita claims about small places, ask how many actual events the rate rests on.
  • ►Ask which question you are actually trying to answer — how much is happening, or how likely it is to happen to someone — and pick the number that answers it rather than the one that was offered.

From the Defense Playbook

Ask for the Denominatorseconds

Whenever you are shown a count ("4,000 complaints", "12 deaths", "9 out of 10 dentists"), ask "out of how many?", because a numerator on its own cannot tell you whether something is common, rare, rising, or falling.

Every playbook entry states how strong its evidence is and when not to use it. Browse the full playbook.

References

  1. Huff, D. (1954). How to Lie with Statistics. W. W. Norton
    Early treatment of choosing the base of a comparison to produce the wanted ranking.
  2. Best, J. (2001). Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists. University of California Press
    How advocates select counts or rates according to the claim, and the practice of asking what a statistic counts and compares.
  3. Spiegelhalter, D. (2019). The Art of Statistics: How to Learn from Data. Pelican
    The discipline of asking about denominators and the instability of rates computed from small populations.
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