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Related Concept Videos

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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In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the direction of association between two variables. The correlation coefficient value ranges from −1 to +1. A value of +1 indicates a perfect positive linear correlation, −1 denotes a perfect negative correlation, and 0 implies no correlation between the two variables. A positive correlation value establishes that as one variable increases, the...
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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. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:
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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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Confirmation Biases01:31

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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According to some social psychologists, people tend to overemphasize internal factors as explanations—or attributions—for the behavior of other people. They tend to assume that the behavior of another person is a trait of that person, and to underestimate the power of the situation on the behavior of others. They tend to fail to recognize when the behavior of another is due to situational variables, and thus to the person’s state. This erroneous assumption is...
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Reducing Bias and Error in the Correlation Coefficient Due to Nonnormality.

Anthony J Bishara1, James B Hittner1

  • 1College of Charleston, Charleston, SC, USA.

Educational and Psychological Measurement
|May 26, 2018
PubMed
Summary

Nonnormal data can inflate Pearson correlation estimates. Alternatives like Spearman and Rankit correlations reduce this bias, offering more reliable results when data deviates from normality.

Keywords:
PearsonSpearmancorrelationnonnormalnormalitytransformation

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Area of Science:

  • Statistics
  • Psychometrics
  • Educational Measurement

Background:

  • Educational and psychological data frequently exhibit nonnormality, deviating from a normal distribution.
  • Nonnormality can introduce bias and errors in point estimates of the Pearson correlation coefficient.
  • Traditional bias adjustments may exacerbate inflation issues under nonnormal conditions.

Purpose of the Study:

  • To evaluate the performance of the Pearson correlation coefficient under nonnormal data conditions.
  • To compare Pearson correlation with alternatives such as Spearman, bootstrap, Box-Cox transformations, and Rankit.
  • To identify robust correlation methods for nonnormal datasets in educational and psychological research.

Main Methods:

  • Monte Carlo simulations were employed to examine correlation coefficients.
  • Data conditions included both normal and various nonnormal distributions, with a focus on heavy-tailed distributions.
  • Performance was assessed by comparing bias and random error across different correlation methods.

Main Results:

  • Nonnormality inflated Pearson correlation estimates by up to +.14, especially with heavy-tailed distributions.
  • Standard bias adjustments worsened the inflation problem.
  • Spearman and Rankit correlations effectively eliminated inflation, yielding conservative estimates.
  • Rankit minimized random error for most sample sizes, while bootstrapping was superior for very small samples (n=10).

Conclusions:

  • The Pearson correlation coefficient is susceptible to inflation and bias when data is nonnormal.
  • Alternatives like Spearman and Rankit correlations are recommended for improved accuracy and reduced bias.
  • Careful selection of correlation methods is crucial when normality assumptions are violated in educational and psychological data analysis.