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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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Statistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. An indirect relationship of the variables signifies a correlation, while a direct relationship shows causation. If it is determined that no connection exists between the variables, then the correlation is a coincidence.
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In statistics, two variables are said to be correlated if the values of one variable are associated with the other variable. Depending on the relationship between two variables, correlation can be of three types– positive correlation, negative correlation, and zero correlation.
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Alfred Binet, along with his student Théophile Simon, was tasked by the French Ministry of Education in 1904 to create a method for identifying students who struggled to learn through conventional classroom instruction. This initiative aimed to address overcrowding by placing such students in specialized schools. Binet and Simon developed an intelligence test comprising 30 tasks, ranging from simple commands, like touching one's nose or ear, to more complex tasks, such as drawing...
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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
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David Wechsler, a psychologist who worked with World War I veterans, developed a significant IQ test in 1939 called the Wechsler-Bellevue Intelligence Scale. This test was innovative because it combined several subtests that measured both verbal and nonverbal skills, reflecting Wechsler's belief that intelligence is a global capacity involving purposeful action, rational thinking, and effective interaction with the environment. This test later evolved into the Wechsler Adult Intelligence...
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Contributions to Estimation of Polychoric Correlations.

Scott Monroe1

  • 1a College of Education , University of Massachusetts Amherst.

Multivariate Behavioral Research
|January 30, 2018
PubMed
Summary

This study introduces a Monte Carlo estimator for the asymptotic covariance matrix (ACM) in structural equation modeling with ordinal data. The new method improves statistical test calibration, especially with smaller sample sizes.

Keywords:
Categorical dataMonte Carlo methodspolychoric correlationstructural equation modeling

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Area of Science:

  • Statistics
  • Psychometrics
  • Quantitative Psychology

Background:

  • Structural equation models (SEMs) are widely used for analyzing complex relationships between variables.
  • Ordinal variables are common in social and behavioral sciences, requiring specialized estimation techniques like polychoric correlations.
  • Multistage estimation in SEMs relies heavily on the asymptotic covariance matrix (ACM) for accurate statistical inference.

Purpose of the Study:

  • To propose and evaluate a novel Monte Carlo estimator for the ACM of polychoric correlation estimates.
  • To assess the impact of violating normality assumptions on SEMs with ordinal data.
  • To compare the performance of the proposed ACM estimator against traditional sample-based methods, particularly in small samples.

Main Methods:

  • Development of a Monte Carlo simulation-based method for estimating the ACM.
  • Conducting simulation studies to evaluate the efficiency and accuracy of the proposed estimator.
  • Investigating the consequences of non-normality in underlying response variables on SEM fit statistics.

Main Results:

  • The proposed Monte Carlo estimator for the ACM demonstrated higher efficiency compared to sample-based estimators, especially in small samples.
  • Improved calibration of overall test statistics was observed when using the Monte Carlo ACM estimator.
  • The study revealed that the impact of non-normality depends on the specific type and characteristics of the thresholds, and overall test statistics showed limited power to detect these non-normality issues.

Conclusions:

  • The Monte Carlo estimation of the ACM offers a more robust alternative to sample-based methods for SEMs with ordinal data, enhancing statistical accuracy.
  • Researchers should be cautious about relying solely on overall test statistics to assess normality assumptions when analyzing ordinal data.
  • The findings provide valuable insights for improving the reliability of structural equation modeling with ordinal variables, particularly in data-limited scenarios.