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Related Concept Videos

Errors In Hypothesis Tests01:14

Errors In Hypothesis Tests

When performing a hypothesis test, there are four possible outcomes depending on the actual truth (or falseness) of the null hypothesis and the decision to reject or not.
Accuracy and Errors in Hypothesis Testing01:13

Accuracy and Errors in Hypothesis Testing

Hypothesis testing is a fundamental statistical tool that begins with the assumption that the null hypothesis H0 is true. During this process, two types of errors can occur: Type I and Type II. A Type I error refers to the incorrect rejection of a true null hypothesis, while a Type II error involves the failure to reject a false null hypothesis.
In hypothesis testing, the probability of making a Type I error, denoted as α, is commonly set at 0.05. This significance level indicates a 5% chance...
Significance Testing: Overview01:04

Significance Testing: Overview

Significance testing is a set of statistical methods used to test whether a claim about a parameter is valid. In analytical chemistry, significance testing is used primarily to determine whether the difference between two values comes from determinate or random errors. The effect of a particular change in the measurement protocol, analyst, or sample itself can cause a deviation from the expected result. In the case of a suspected deviation/outlier, we need to be able to confirm mathematically...
Random Error01:04

Random Error

Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument imperfections, or the inherent variability of the phenomena being measured. Usually, these errors cannot be predicted, estimated, or characterized because their direction and magnitude often vary in magnitude and direction even during consecutive measurements. As a result, they are difficult to eliminate. However, the aggregate effect of these errors can be...
Random and Systematic Errors01:20

Random and Systematic Errors

Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...
Random and Systematic Errors01:20

Random and Systematic Errors

Scientists always try their best to record measurements with the utmost accuracy and precision. However, sometimes errors do occur. These errors can be random or systematic. Random errors are observed due to the inconsistency or fluctuation in the measurement process, or variations in the quantity itself that is being measured. Such errors fluctuate from being greater than or less than the true value in repeated measurements. Consider a scientist measuring the length of an earthworm using a...

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Related Experiment Video

Updated: May 31, 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

Published on: July 3, 2020

A note on type II error under random effects misspecification in generalized linear mixed models.

John M Neuhaus1, Charles E McCulloch, Ross Boylan

  • 1Department of Epidemiology and Biostatistics, University of California, San Francisco, California 94143-0560, USA. john@biostat.ucsf.edu

Biometrics
|June 22, 2011
PubMed
Summary
This summary is machine-generated.

Misspecification of random effects distribution in generalized linear mixed models has minimal impact on Type II error rates. Our corrected simulations show little increase in Type II error, contradicting previous claims.

Related Experiment Videos

Last Updated: May 31, 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

Published on: July 3, 2020

Area of Science:

  • Statistics
  • Biostatistics
  • Statistical Modeling

Background:

  • Generalized linear mixed models (GLMMs) are widely used in various scientific fields.
  • The impact of misspecifying the random effects distribution in GLMMs on statistical inference remains a topic of investigation.
  • Previous studies suggested significant consequences of such misspecification on Type II error rates.

Purpose of the Study:

  • To re-evaluate the claim that misspecification of the random effects distribution shape in GLMMs markedly increases Type II error.
  • To present logically sound simulation studies to assess the robustness of GLMM tests to distributional misspecification.
  • To provide accurate insights into the impact of random effects distribution misspecification on statistical power.

Main Methods:

  • Conducting simulation studies using generalized linear mixed models.
  • Implementing corrected analytical approaches to address a logical fallacy in prior research.
  • Comparing Type II error rates under various scenarios of random effects distribution misspecification.

Main Results:

  • Logically sound simulation studies demonstrate a negligible increase in Type II error rates.
  • The findings contradict the assertion that misspecification of random effects distribution shape leads to substantial decreases in statistical power.
  • Results align with earlier research indicating minimal impact of such misspecification.

Conclusions:

  • Misspecification of the random effects distribution shape in GLMMs has a limited effect on Type II error rates.
  • The robustness of tests based on GLMM fits to distributional misspecification is greater than previously suggested.
  • Accurate simulation studies are crucial for reliable statistical inference in mixed-effects modeling.