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Related Concept Videos

Random Error01:04

Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
Bias01:22

Bias

Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected or encouraged over others in sampling or testing. Bias can occur during any research phase, including study design, data collection, analysis, and publication.
In statistics, a sampling bias is created when a sample is collected from a population, and some members of the population are not as likely to be chosen as others (remember, each member...
Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and 0s. In...
Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
The test works...
Probability in Statistics01:14

Probability in Statistics

Probability is the likelihood of an event occurring. The term event is defined as a collection of results of a procedure. An event is a simple event when an outcome cannot be divided into simpler parts.
An example of a simple event is a coin toss. The result of a coin toss is either a head or a tail. Here, head and tail are two simple events. These two simple events make up the sample space. Further, the probability of an event occurring falls within the range of 0 to 1. The probability of an...
Statistical Significance01:37

Statistical Significance

Once data is collected from both the experimental and the control groups, a statistical analysis is conducted to find out if there are meaningful differences between the two groups. A statistical analysis determines how likely any difference found is due to chance (and thus not meaningful). In psychology, group differences are considered meaningful, or significant, if the odds that these differences occurred by chance alone are 5 percent or less. Stated another way, if we repeated this...

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Related Experiment Video

Updated: May 12, 2026

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
08:12

A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments

Published on: March 1, 2022

Why are people bad at detecting randomness? A statistical argument.

Joseph J Williams1, Thomas L Griffiths

  • 1Department of Psychology, University of California, Berkeley.

Journal of Experimental Psychology. Learning, Memory, and Cognition
|April 24, 2013
PubMed
Summary
This summary is machine-generated.

Detecting randomness is difficult because random sequences provide weak evidence. This statistical challenge, not just misconceptions, explains errors in judging randomness.

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Area of Science:

  • Cognitive Psychology
  • Statistical Inference
  • Decision Making

Background:

  • Errors in detecting randomness are often attributed to cognitive biases and misconceptions.
  • Existing explanations do not fully account for the inherent statistical properties of random processes.

Purpose of the Study:

  • To propose and provide evidence for an account of randomness detection errors based on statistical difficulty.
  • To investigate how the nested nature of randomness within systematicity affects judgments of random sequences.

Main Methods:

  • Bayesian statistical analysis to model the relationship between random and systematic processes.
  • Three experiments involving judgments of sequences of coin flips for randomness, bias, and sequential dependence.

Main Results:

  • Random sequences provide weak statistical evidence, making them only weakly diagnostic of a random process.
  • Low accuracy in judging randomness stems from this weak evidence, not solely from misconceptions.
  • Equating evidence strength eliminated accuracy differences between nested and non-nested hypothesis judgments.

Conclusions:

  • The inherent statistical difficulty of identifying random processes significantly contributes to errors in randomness detection.
  • Understanding the statistical evidence distribution is crucial for complementing existing explanations of misconceptions.
  • This account offers a more comprehensive explanation for errors in judging randomness.