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Related Concept Videos

Expected Value01:15

Expected Value

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The expected value is known as the "long-term" average or mean. This means that over the long term of experimenting over and over, you would expect this average. The expected average is represented by the symbol μ. It is calculated as follows:
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Random Error01:04

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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...
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Unusual Results01:16

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Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ  from the mean, μ  is considered unusual.
Maximum unusual value =...
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Regression Toward the Mean01:52

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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Uncertainty in Measurement: Accuracy and Precision03:37

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Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value. 
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Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
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Are random events expected to be small?

Karl Halvor Teigen1, Alf Børre Kanten2

  • 1Department of Psychology, University of Oslo, Oslo, Norway. k.h.teigen@psykologi.uio.no.

Psychological Research
|October 2, 2019
PubMed
Summary

People intuitively associate randomness with small events, not large ones. This perception of chance influences how we interpret everyday occurrences and even scientific concepts.

Area of Science:

  • Cognitive Science
  • Psychology
  • Statistics

Background:

  • Intuitions about probability and randomness often deviate from formal definitions.
  • The concept of randomness is frequently linked to events occurring "by chance" or "accidentally".

Purpose of the Study:

  • To test the hypothesis that perceived randomness is associated with the size of events.
  • To investigate whether people associate chance occurrences more with small than large outcomes.

Main Methods:

  • Five experiments were conducted to examine the relationship between perceived randomness and size.
  • Participants evaluated statements about chance, interpreted stories of random events, and assessed the randomness of graphical representations and animal behavior based on size.

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Main Results:

  • Small outcomes attributed to chance were perceived as more natural than large outcomes.
  • Stories of randomness were preferred to start with small events, regardless of eventual significance.
  • Small changes in random walks and the behavior of small animals were seen as more random than large changes or larger animals.

Conclusions:

  • A pervasive association exists between smallness and perceived randomness in human intuition.
  • This cognitive bias may stem from real-world observations and inherent cognitive constraints.