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Related Concept Videos

Introduction to Test of Independence01:21

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
Coefficient of Correlation01:12

Coefficient of Correlation

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 strength of the linear...
Calculating and Interpreting the Linear Correlation Coefficient01:11

Calculating and Interpreting the Linear Correlation Coefficient

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:
Bonferroni Test01:10

Bonferroni Test

The Bonferroni test is a statistical test named after Carlo Emilio Bonferroni, an Italian mathematician best known for Bonferroni inequalities. This statistical test is a type of multiple comparison test to determine which means are different than the rest. Bonferroni test can minimize the Type 1 error by reducing the significance level alpha, which otherwise increases with sample pairs.
The means of different samples are first paired in all possible combinations.
The null hypothesis of the...
Calibration Curves: Correlation Coefficient01:10

Calibration Curves: Correlation Coefficient

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 other increases, and...
Odds Ratio01:09

Odds Ratio

The odds ratio (OR) is a statistical measure used extensively in epidemiology and research to quantify the strength of association between exposure and outcome across different groups. Unlike relative risk, which compares the probabilities of an event occurring, the odds ratio compares the odds of an event occurring in the exposed group to the odds of it occurring in the unexposed group. The odds, in this context, are calculated as the probability of the event happening divided by the...

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Related Experiment Video

Updated: Jul 15, 2026

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

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Power calculation for the likelihood ratio-test when comparing two dependent intraclass correlation coefficients.

B Giraudeau1, R Porcher, J Y Mary

  • 1INSERM CIC 202, Faculté de Médecine, 10 Bd Tonnellé, BP 3223, 37032 Tours Cedex 1, France. giraudeau@med.univ-tours.fr

Computer Methods and Programs in Biomedicine
|January 18, 2005
PubMed
Summary

This study introduces statistical methods for comparing the reproducibility of two devices using dependent intraclass correlation coefficients (ICCs). The developed macros aid in planning reproducibility studies by calculating the necessary number of subjects and replicates for power analysis.

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Area of Science:

  • Biostatistics
  • Medical Device Evaluation
  • Statistical Methodology

Background:

  • Reproducibility studies are crucial for evaluating the consistency of measurements from medical devices.
  • Comparing two devices requires assessing dependent intraclass correlation coefficients (ICCs) on a single subject sample.
  • Sample size and replicate number are key planning parameters for such studies.

Purpose of the Study:

  • To develop and propose statistical tools for power calculations in reproducibility studies comparing two devices.
  • To enable researchers to determine optimal sample sizes and replicate numbers for robust study design.

Main Methods:

  • Development of SAS and S-plus macros for power calculations.
  • Implementation of a simulation study to compare dependent ICCs.
  • Utilizing a likelihood ratio-test for comparing the dependent ICCs.

Main Results:

  • The proposed macros facilitate power calculations for comparing dependent ICCs.
  • Simulation results support the utility of the macros in study planning.
  • The likelihood ratio-test provides a method for comparing ICCs derived from dependent measurements.

Conclusions:

  • The developed macros offer a valuable resource for planning rigorous reproducibility studies.
  • Accurate power calculations ensure adequate sample sizes and replicates for reliable device comparison.
  • This methodology enhances the statistical foundation for medical device evaluation.