Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Fisher's Exact Test01:08

Fisher's Exact Test

871
Fisher's exact test is a statistical significance test widely used to analyze 2x2 contingency tables, particularly in situations where sample sizes are small. Unlike the chi-squared test, which approximates P-values and assumes minimum expected frequencies of at least five in each cell, Fisher's exact test calculates the exact probability (P-value) of observing the data or more extreme results under the null hypothesis. This feature makes it especially valuable when the assumptions of...
871
Friedman Two-way Analysis of Variance by Ranks01:21

Friedman Two-way Analysis of Variance by Ranks

331
Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
331
F Distribution01:19

F Distribution

5.0K
The F distribution was named after Sir Ronald Fisher, an English statistician. The F statistic is a ratio (a fraction) with two sets of degrees of freedom; one for the numerator and one for the denominator. The F distribution is derived from the Student's t distribution. The values of the F distribution are squares of the corresponding values of the t distribution. One-Way ANOVA expands the t test for comparing more than two groups. The scope of that derivation is beyond the level of this...
5.0K
Behrens–Fisher Test00:57

Behrens–Fisher Test

146
The Behrens-Fisher test is a statistical method designed to address the Behrens-Fisher problem, which arises when comparing the means of two normally distributed populations with unequal variances. Unlike the Student's t-test, which assumes equal variances, the Behrens-Fisher test allows for mean comparison without this restrictive assumption. This flexibility makes it particularly valuable in scenarios where two independent samples exhibit normality but lack variance homogeneity.
This test...
146
Two-Way ANOVA01:17

Two-Way ANOVA

2.8K
The two-way ANOVA is an extension of the one-way ANOVA. It is a statistical test performed on three or more samples categorized by two factors - a row factor and a column factor. Ronald Fischer mentioned it in 1925 in his book 'Statistical Methods for Researchers.'
The two-way ANOVA analysis initially begins by stating the null hypothesis that there is an interaction effect between the two factors of a dataset. This effect can be visualized using line segments formed by joining the...
2.8K
Factorial Design02:01

Factorial Design

13.4K
Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable due to more than one independent variable, also known as factors. Changes in worker productivity can be reasoned, for example, to be influenced by salary and other conditions, such as skill level. One way to test this hypothesis is by categorizing salary into three levels (low, moderate, and high) and skills sets into two levels (entry level...
13.4K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Excessive Censoring Degrades Individual-Specific Cortical Parcellations and Personalized TMS Targets.

bioRxiv : the preprint server for biology·2026
Same author

Effect sizes in human functional neuroimaging.

Research square·2026
Same author

The Hidden Landscape of Missed Effects in Human Functional Neuroimaging.

bioRxiv : the preprint server for biology·2026
Same author

Widespread use of invalid statistical tests in biomedical machine learning.

bioRxiv : the preprint server for biology·2026
Same author

Scalable Bayesian Image-on-Scalar Regression for Population-Scale Neuroimaging Data Analysis.

Journal of the American Statistical Association·2026
Same author

Convergent and divergent brain-cognition development in early adolescence.

Nature communications·2026

Related Experiment Video

Updated: Oct 14, 2025

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

Published on: July 3, 2020

3.5K

Fisher Scoring for crossed factor linear mixed models.

Thomas Maullin-Sapey1, Thomas E Nichols1

  • 1Big Data Institute, Li Ka Shing Centre for Health Information and Discovery, Old Road Campus, Oxford, OX3 7LF UK.

Statistics and Computing
|November 1, 2021
PubMed
Summary

This study extends the Fisher Scoring algorithm for linear mixed models (LMMs) to handle complex multi-factor data, improving parameter estimation and offering a novel, efficient method for Satterthwaite degrees of freedom estimation.

Keywords:
Crossed factorsFisher ScoringLinear mixed model

More Related Videos

Using the FishSim Animation Toolchain to Investigate Fish Behavior: A Case Study on Mate-Choice Copying In Sailfin Mollies
10:50

Using the FishSim Animation Toolchain to Investigate Fish Behavior: A Case Study on Mate-Choice Copying In Sailfin Mollies

Published on: November 8, 2018

11.0K
Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
06:52

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

6.4K

Related Experiment Videos

Last Updated: Oct 14, 2025

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

Published on: July 3, 2020

3.5K
Using the FishSim Animation Toolchain to Investigate Fish Behavior: A Case Study on Mate-Choice Copying In Sailfin Mollies
10:50

Using the FishSim Animation Toolchain to Investigate Fish Behavior: A Case Study on Mate-Choice Copying In Sailfin Mollies

Published on: November 8, 2018

11.0K
Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
06:52

Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills

Published on: September 17, 2019

6.4K

Area of Science:

  • Statistics
  • Biostatistics
  • Data Analysis

Background:

  • Linear mixed models (LMMs) are crucial for analyzing longitudinal, heterogeneous, or unbalanced clustered data.
  • Traditional LMM research focused on single-factor designs, but recent work emphasizes multi-factor designs.

Purpose of the Study:

  • To extend the Fisher Scoring algorithm for parameter estimation in multi-factor linear mixed models.
  • To develop a new analytical method for Satterthwaite degrees of freedom estimation in LMMs.

Main Methods:

  • Derived new expressions for extending Fisher Scoring to multiple, crossed-factor LMM designs.
  • Compared five Fisher Scoring variants against the R package lme4 using simulations and real data.
  • Developed an analytical method for Satterthwaite degrees of freedom estimation, avoiding iterative gradient estimation.

Main Results:

  • Four of the five proposed Fisher Scoring variants demonstrated correctness and computational efficiency.
  • The new analytical method for Satterthwaite degrees of freedom estimation yielded lower bias and variance compared to existing methods.

Conclusions:

  • The extended Fisher Scoring algorithms are effective for multi-factor LMMs.
  • The novel analytical approach significantly improves Satterthwaite degrees of freedom estimation accuracy and efficiency.