Related Experiment Video
Updated: May 16, 2026

Experimental and Data Analysis Workflow for Soft Matter Nanoindentation
Published on: January 18, 2022
An applied examination of different weighting methods for the root expected mean square difference and root mean
1Research and Evaluation Methodology, School of Human Development and Organizational Studies in Education, University of Florida, 1215 Norman Hall, Gainesville, FL 32611, USA. ahuggins@coe.ufl.edu
Abstract:
It is possible that functions used to link tests are sensitive to subpopulations of test takers. The REMSD and RMSD(x) are weighted effect sizes of linking invariance, yet it is often unclear how the weights are most appropriately applied when subpopulation group sizes are heterogeneous. The objective of this research is to apply two different weighting methods to the REMSD and RMSD(x) functions while testing for population invariance in a linkage across subpopulations of disparate sample sizes, and to subsequently compare the results across these differentially weighted effect sizes. The findings demonstrate that utilizing proportional weights in the REMSD and RMSD(x) indices can underestimate differences in linking functions for small subpopulations.
Related Concept Videos
Weighted Mean
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
Root Mean Square
For example, consider the velocity of gas molecules in a container. The gas molecules are moving in different directions, which might impart positive and negative...
Testing a Claim about Standard Deviation
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...
One-Way ANOVA: Unequal Sample Sizes
Comparing Experimental Results: Student's t-Test
Variation: Normal Distribution, Range, and Standard Deviation