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Statistical Illusions

Entirely true figures pointing at an entirely false conclusion.

  • 12 / 12
  • No visual on file
    Statistical Illusions Entry #0441

    The reason per capita reverses many rankings

    Dividing by population removes size from a comparison. Since size drives most totals, the ranking that survives is often the opposite of the original.

    Adept
    The hidden part #0441

    A total measures magnitude and a rate measures intensity. Which one is published decides most of the ranking.

    Open file
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    Statistical Illusions Entry #0440

    Why counting something changes what gets counted

    A measure requires a definition, and once the measure is consequential the definition becomes something to be managed rather than merely applied.

    Master
    The hidden part #0440

    A number is a definition applied to the world. Make the number consequential and the definition becomes the thing under negotiation.

    Open file
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    Statistical Illusions Entry #0439

    The reason a forecast range matters more than its midpoint

    A single number implies a precision the forecast does not have. The width of the interval is the part that says how much the forecast actually knows.

    Adept
    The hidden part #0439

    Two forecasts with the same midpoint and different widths are different forecasts. Only one of those numbers usually survives.

    Open file
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    Statistical Illusions Entry #0438

    Why the median rent tells you more than the average

    A mean is pulled by every extreme value in the set. A median is not, so for skewed quantities it describes the ordinary case far more closely.

    Novice
    The hidden part #0438

    A mean answers a question about the total. For a skewed quantity, only the median approximates the ordinary case.

    Open file
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    Statistical Illusions Entry #0450

    Why the missing data is the most informative column

    Absence has a shape. Which records lack a value is usually related to what the value would have been, so dropping them changes the population.

    Adept
    The hidden part #0450

    If presence depends on the value, dropping incomplete rows selects on the variable of interest. Model the missingness — it is often the better predictor.

    Open file
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    Statistical Illusions Entry #0449

    The reason a benchmark becomes a distortion

    A published comparison reorganises the thing it measures. Effort moves to the scored dimensions, and the unscored ones become where the cost is paid.

    Master
    The hidden part #0449

    Publishing a comparison makes it an intervention. Effort migrates to the scored dimensions, and the unscored ones have no series to show the loss.

    Open file
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    Statistical Illusions Entry #0448

    Why a rounded figure travels further than a precise one

    Transmission selects for what can be repeated without effort. A round number survives the retelling; the decimal is dropped at the first hop.

    Adept
    The hidden part #0448

    Retelling is a memory task, and round numbers are cheaper to store and produce. Precision is lost by selection, not by dishonesty.

    Open file
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    Statistical Illusions Entry #0447

    The reason a compound rate deceives over long periods

    People extend growth in straight lines because that is what intuition supplies. The gap between the line and the curve is where the surprise lives.

    Adept
    The hidden part #0447

    Intuition extrapolates by addition and the process multiplies. Short horizons reward the habit, and long ones are where it fails.

    Open file
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    Statistical Illusions Entry #0446

    Why a lagging statistic invites the wrong correction

    The number describes a situation that has already moved. Acting hard on it applies force in the direction the system has just finished going.

    Novice
    The hidden part #0446

    When the measurement lag matches the system’s response time, a proportional correction becomes an oscillation. Each step is defensible; the sequence is not.

    Open file
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    Statistical Illusions Entry #0445

    The reason a self-selected panel overstates strong opinions

    Answering costs time, and the people who pay it are those with something to say. Indifference is the hardest state to get into a dataset.

    Master
    The hidden part #0445

    Willingness to answer is itself an attitude, and weighting cannot repair it. Indifference is the state a voluntary survey cannot record.

    Open file
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    Statistical Illusions Entry #0444

    Why the sample frame decides the result

    Sampling errors shrink with size; frame errors do not. If the list you draw from excludes a group, no amount of sampling from it will find them.

    Adept
    The hidden part #0444

    Size shrinks sampling error and leaves coverage error untouched. A precise estimate of a frame is not an estimate of a population.

    Open file
  • No visual on file
    Statistical Illusions Entry #0443

    The reason a leading indicator stops leading

    It led because of a structure that produced the delay. When the structure changes, the correlation stays in the historical data and leaves the future.

    Novice
    The hidden part #0443

    An indicator leads because of a structure, not because of its history. Fit is measured with data nobody had at the time.

    Open file