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Related Concept Videos

Uncertainty: Confidence Intervals00:54

Uncertainty: Confidence Intervals

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The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The interpretation of a 95% confidence interval, for instance, is that the statistician is 95% confident that the true mean falls within the interval. The upper and lower limits of this range are known as confidence limits. The confidence limits for the true mean are estimated from the sample's mean, the standard deviation, and the statistical factor...
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Confidence Intervals01:21

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An unbiased point estimate is often insufficient to predict a population estimate, such as population mean or population proportion. In this scenario, a confidence interval is used. A confidence interval is an estimate similar to a  sample proportion. However, unlike the point estimate which is a single value, the confidence interval  contains a range of values. These values have lower and upper limits, known as confidence limits, and can be designated as L1 and L2, respectively.
A...
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Interpretation of Confidence Intervals01:19

Interpretation of Confidence Intervals

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A confidence interval is a better estimate of the population than a point estimate, as it uses a range of values from a sample instead of a single value.
Confidence intervals have confidence coefficients that are crucial for their interpretation. The most common confidence coefficients are 0.90, 0.95, and 0.99, which can be written as percentages–90%, 95%, and 99%, respectively.
Suppose a person calculates a confidence interval with a confidence coefficient of 0.95. In that case, they can...
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Confidence Coefficient01:24

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The confidence coefficient is also known as the confidence level or degree of confidence. It is the percent expression for the probability, 1-α, that the confidence interval contains the true population parameter assuming that the confidence interval is obtained after sufficient unbiased sampling; for example, if the CL = 90%, then in 90 out of 100 samples the interval estimate will enclose the true population parameter. Here α is the area under the curve, distributed equally under...
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Confidence Interval for Estimating Population Mean01:25

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A point estimate of the population mean is obtained from a single sample. Such a point estimate does not represent a population well because it needs to account for variability in the population. Single point estimate can also be biased despite the sample being selected randomly. Thus, a point estimate is often unreliable. A confidence interval is needed to reduce this unreliability.
A confidence interval for the mean is a range of values that provides an estimate of the population mean. As the...
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Confirmation Biases

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The confirmation bias is the tendency to focus on information that confirms our existing beliefs and ignore information that is inconsistent with our expectations. For example, if you think that your professor is not very nice, you notice all of the instances of rude behavior exhibited by the professor while ignoring the countless pleasant interactions he is involved in on a daily basis. Have you ever fallen prey to the confirmation bias, either as the source or target of such bias?
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Related Experiment Video

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The Collective Trust Game: An Online Group Adaptation of the Trust Game Based on the HoneyComb Paradigm
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Opinion formation with time-varying bounded confidence.

YunHong Zhang1,2, QiPeng Liu1, SiYing Zhang1

  • 1Institute of Complexity Science, Qingdao University, Qingdao, China.

Plos One
|March 7, 2017
PubMed
Summary

Individuals adjust their opinions based on peer influence, a process modeled by time-varying bounded confidence. Greater confidence variation leads to stronger neighbor influence and faster opinion evolution towards consensus.

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Area of Science:

  • Social Dynamics
  • Network Science
  • Computational Social Science

Background:

  • Individuals in social groups often adapt their opinions to align with those of their neighbors.
  • This peer influence affects an individual's bounded confidence threshold, which governs opinion revision.

Purpose of the Study:

  • To propose and analyze an opinion dynamics model incorporating time-varying bounded confidence.
  • To investigate how individual confidence variation and network structure influence opinion evolution and consensus formation.

Main Methods:

  • Development of a novel opinion dynamics model with time-varying bounded confidence.
  • Simulation of opinion evolution on a directed network where the bounded confidence threshold is dynamically determined.
  • Analysis of the impact of confidence variation and network topology (in/out degree) on opinion convergence.

Main Results:

  • Group opinions exhibit exponential convergence to consensus when neighbor relationships are stable.
  • Individual opinion evolution is significantly influenced by the average opinion strength of neighbors.
  • Increased confidence variation amplifies the impact on opinion evolution and accelerates convergence.

Conclusions:

  • The proposed model captures the interplay between individual confidence, peer influence, and network structure in shaping collective opinion.
  • Confidence variation is a critical factor driving opinion dynamics and the formation of consensus within social networks.