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Related Concept Videos

Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

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The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
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Coefficient of Correlation01:12

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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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Calibration Curves: Correlation Coefficient01:10

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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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Estimating Population Standard Deviation01:26

Estimating Population Standard Deviation

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When the population standard deviation is unknown and the sample size is large, the sample standard deviation s is commonly used as a point estimate of σ. However, it can sometimes under or overestimate the population standard deviation. To overcome this drawback, confidence intervals are determined to estimate population parameters and eliminate any calculation bias accurately. However, this only applies to random samples from normally distributed populations. Knowing the sample mean and...
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Estimating Population Mean with Known Standard Deviation01:16

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To construct a confidence interval for a single unknown population mean μ, where the population standard deviation is known, we need sample mean as an estimate for μ and we need the margin of error. Here, the margin of error (EBM) is called the error bound for a population mean (abbreviated EBM). The sample mean is the point estimate of the unknown population mean μ.
The confidence interval estimate will have the form as follows:
(point estimate - error bound, point estimate +...
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Sequential accuracy in parameter estimation for population correlation coefficients.

Ken Kelley1, Francis Bilson Darku1, Bhargab Chattopadhyay2

  • 1Department of Information Technology, Analytics, and Operations, Mendoza College of Business, University of Notre Dame.

Psychological Methods
|March 5, 2019
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Summary
This summary is machine-generated.

Researchers developed new methods for narrow confidence intervals for correlation coefficients like Pearson's r, Kendall's tau, and Spearman's rho. These sequential estimation procedures avoid needing unknown population values for accurate study design.

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Area of Science:

  • Psychometrics and Quantitative Psychology
  • Statistical Methods in Research

Background:

  • Correlation coefficients are crucial effect size measures in psychology for quantifying variable relationships.
  • Existing methods for designing studies on correlation coefficients often rely on unknown population parameters.
  • Accurate confidence intervals are essential for reliable effect size estimation.

Purpose of the Study:

  • To develop novel methods for constructing narrow confidence intervals for population correlation coefficients.
  • To address the limitation of existing methods that require unknowable population values.
  • To provide a distribution-free approach for confidence interval construction.

Main Methods:

  • Development of sequential estimation procedures for Pearson's r, Kendall's tau, and Spearman's rho.
  • Implementation of stopping rules to determine sample size adaptively.
  • Extension of methods to the squared multiple correlation coefficient under multivariate normality.

Main Results:

  • The proposed sequential methods successfully construct confidence intervals with specified width and confidence levels.
  • These procedures do not require prior knowledge of population parameters, unlike traditional methods.
  • Monte Carlo simulations confirmed the effectiveness of the sequential approach.

Conclusions:

  • Sequential estimation offers a robust and practical solution for designing studies requiring narrow confidence intervals for correlation coefficients.
  • The developed methods enhance the reliability of effect size estimation in psychological research.
  • Freely available R code in the MBESS package facilitates the implementation of these advanced statistical techniques.