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Inferring an unobservable population size from observable samples.

Jack Cao1, Mahzarin R Banaji2

  • 1Department of Psychology, Harvard University, Cambridge, MA, USA. jackcao@fas.harvard.edu.

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People accurately infer population size from samples when the sample suggests a large population. However, they are biased when samples suggest a small population, showing overconfidence in inaccurate judgments.

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AccuracyConfidenceNumerical cognitionPopulation estimatesSampling processes

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Area of Science:

  • Cognitive Psychology
  • Social Psychology
  • Behavioral Economics

Background:

  • Estimating population size is crucial for physical and social success.
  • Direct population assessment is often impossible, necessitating inference from samples.
  • Previous research suggested limitations in human statistical reasoning and sample size insensitivity.

Purpose of the Study:

  • To investigate people's ability to infer unobservable population sizes from observable samples.
  • To examine the accuracy and confidence associated with these population size inferences.
  • To understand the cognitive and metacognitive factors influencing statistical judgment.

Main Methods:

  • Participants made inferences about population sizes based on observable sample data.
  • Accuracy of inferences was compared against actual population sizes.
  • Confidence levels in these inferences were recorded.
  • A manipulation was introduced to alter inference magnitude and variability.

Main Results:

  • Inferences were accurate when sample data indicated a large population.
  • Systematic biases emerged when sample data indicated a small population.
  • Confidence in inferences was highest when accuracy was lowest, indicating a metacognitive failure.
  • Manipulation of inference magnitude did not affect confidence levels.

Conclusions:

  • Human statistical inference is adept but has specific limitations, particularly with small inferred populations.
  • A dissociation between cognitive accuracy and metacognitive confidence exists.
  • Metacognitive overconfidence can occur even when statistical reasoning is flawed.