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Random and Systematic Errors

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Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...

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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

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Random variation and systematic biases in probability estimation.

Rita Howe¹, Fintan Costello¹

¹School of Computer Science, University College Dublin, Ireland.

Cognitive Psychology

|November 14, 2020

Summary

This summary is machine-generated.

Random variation in probabilistic reasoning explains common biases like the conjunction and disjunction fallacies. This study quantifies this random noise, showing it follows a binomial distribution, supporting a frequentist model of human probability judgment.

Keywords:

Conjunction fallacy Disjunction fallacy Noise Probability estimation Variance

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Area of Science:

Cognitive Psychology
Decision Science
Probability Theory

Background:

Systematic biases in probabilistic reasoning are often attributed to random variation.
Previous theories assume sufficient random variation exists but lack empirical examination.
Understanding the nature of this random variation is crucial for explaining cognitive biases.

Purpose of the Study:

To investigate the degree, level, and properties of random variation in human probability judgments.
To determine if random variation can account for specific probabilistic reasoning fallacies.
To identify the mathematical model governing random variation in probability judgments.

Main Methods:

Conducted four experiments on people's probability judgments.
Quantified the degree and level of random variance in judgment.
Analyzed the characteristic properties of this random variation.
Tested predictions against established probability theory models.

Main Results:

The degree of random variance in probability judgments is sufficient to explain the conjunction and disjunction fallacies.
The level of variance reliably predicts the occurrence of these fallacies.
Random variance in probability judgments follows the binomial proportion distribution.
This suggests human probabilistic reasoning is frequentist but subject to random noise.

Conclusions:

Random variation, not just systematic errors, plays a key role in probabilistic reasoning fallacies.
The binomial proportion distribution provides a mathematical framework for understanding this random variation.
Findings support a model where frequentist probability principles are modulated by random noise in human judgment.