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Related Concept Videos

Correlations02:20

Correlations

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Correlation means that there is a relationship between two or more variables (such as ice cream consumption and crime), but this relationship does not necessarily imply cause and effect. When two variables are correlated, it simply means that as one variable changes, so does the other. We can measure correlation by calculating a statistic known as a correlation coefficient. A correlation coefficient is a number from -1 to +1 that indicates the strength and direction of the relationship between...
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Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

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An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...
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Cause and Effect01:53

Cause and Effect

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While variables are sometimes correlated because one does cause the other, it could also be that some other factor, a confounding variable, is actually causing the systematic movement in our variables of interest. For instance, as sales in ice cream increase, so does the overall rate of crime. Is it possible that indulging in your favorite flavor of ice cream could send you on a crime spree? Or, after committing crime do you think you might decide to treat yourself to a cone?
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Sign Test for Matched Pairs01:17

Sign Test for Matched Pairs

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The sign test for matched pairs offers a robust method for comparing two paired samples, often for the effects of an intervention in one of them. This method is very useful in situations where the underlying distribution of the data is unknown. The test compares two related samples—often pre- and post-treatment measurements on the same subjects—to determine if there are significant differences in their median values.
To conduct the sign test, we first calculate the differences in...
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Confidence Coefficient01:24

Confidence Coefficient

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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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Coefficient of Correlation01:12

Coefficient of Correlation

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The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable x and the dependent variable y.
If you suspect a linear relationship between x and y, then r can measure how strong the linear relationship is.
What the VALUE of r tells us:
The value of r is always between –1 and +1: –1 ≤ r ≤ 1.
The size of the correlation r indicates the...
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Related Experiment Video

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Using Informational Connectivity to Measure the Synchronous Emergence of fMRI Multi-voxel Information Across Time
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On Suspicious Coincidences and Pointwise Mutual Information.

Christopher K I Williams1

  • 1School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, U.K. ckiw@inf.ed.ac.uk.

Neural Computation
|August 26, 2022
PubMed
Summary

This study examines measures of association for detecting suspicious event co-occurrences. Pointwise mutual information (PMI) is sensitive to marginal probabilities, potentially inflating scores for rare events.

Area of Science:

  • Statistics
  • Data Analysis
  • Probability Theory

Background:

  • The concept of
  • suspicious
  • co-occurrence of events A and B was proposed by Barlow (1985) when P(A,B) is significantly greater than the product of their individual probabilities P(A)P(B).
  • Classical measures of association for 2 × 2 contingency tables are essential for quantifying relationships between binary variables.

Purpose of the Study:

  • To review and compare classical measures of association for 2 × 2 contingency tables.
  • To analyze the behavior of mutual information (MI) and pointwise mutual information (PMI) as measures of association.
  • To evaluate the suitability of PMI for flagging suspicious coincidences, considering its sensitivity to marginal probabilities.

Main Methods:

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  • Review of established statistical measures like Yule's Y.
  • Analysis of mutual information (MI) and pointwise mutual information (PMI) based on probability ratios.
  • Comparison of MI and PMI behavior with Yule's Y after accounting for marginal effects.

Main Results:

  • Yule's Y is independent of marginal probabilities, depending solely on the odds ratio (λ).
  • Mutual information (MI) and pointwise mutual information (PMI) are functions of the ratio P(A,B)/P(A)P(B).
  • After controlling for marginal effects, MI and PMI exhibit similar functional behavior to Yule's Y concerning the odds ratio (λ).

Conclusions:

  • Pointwise mutual information (PMI) is widely used for identifying suspicious coincidences.
  • The sensitivity of PMI to marginal probabilities can lead to inflated scores for sparse events.
  • Careful consideration of marginal effects is crucial when using PMI to assess event co-occurrence.