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Related Concept Videos

Critical Region, Critical Values and Significance Level01:16

Critical Region, Critical Values and Significance Level

The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
In hypothesis testing, a sample statistic is converted to a test statistic using z, t, or chi-square distribution. A critical region is an area under the curve in  probability distributions demarcated by the critical value. When the test statistic falls in this region, it suggests that the null hypothesis must be rejected. As this region contains all those values of the test...
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...
Decision Making: Traditional Method01:14

Decision Making: Traditional Method

The process of hypothesis testing based on the traditional method includes calculating the critical value, testing the value of the test statistic using the sample data, and interpreting these values.
First, a specific claim about the population parameter is decided based on the research question and is stated in a simple form. Further, an opposing statement to this claim is also stated. These statements can act as null and alternative hypotheses, out of which a null hypothesis would be a...
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...
Statistical Significance01:37

Statistical Significance

Once data is collected from both the experimental and the control groups, a statistical analysis is conducted to find out if there are meaningful differences between the two groups. A statistical analysis determines how likely any difference found is due to chance (and thus not meaningful). In psychology, group differences are considered meaningful, or significant, if the odds that these differences occurred by chance alone are 5 percent or less. Stated another way, if we repeated this...
Introduction to the Sign Test01:10

Introduction to the Sign Test

The sign test is an important tool in nonparametric statistics, offering a straightforward yet effective method for analyzing matched pairs, nominal data, or hypotheses concerning the median of a population. It transforms data points into positive or negative signs, avoiding the need for assumptions about data distribution and instead focusing on the direction of change. It is particularly valuable when data does not conform to the normal distribution requirements of many parametric tests. For...

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

Published on: July 3, 2020

Solutions for Determining the Significance Region Using the Johnson-Neyman Type Procedure in Generalized Linear

Ann A Lazar1, Gary O Zerbe

  • 1University of California, San Francisco.

Journal of Educational and Behavioral Statistics : a Quarterly Publication Sponsored by the American Educational Research Association and the American Statistical Association
|June 18, 2013
PubMed
Summary
This summary is machine-generated.

This study introduces new methods for finding significance regions in generalized linear (mixed) models (GLM/GLMM). These methods overcome limitations of existing procedures for non-normal data and improve accuracy.

Keywords:
generalized estimating equationshierarchical linear modelslongitudinal analysismultiple testingsimultaneous testing

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Area of Science:

  • Statistics
  • Biostatistics
  • Regression Analysis

Background:

  • Comparing regression curves across groups is common in research.
  • Determining the
  • significance region
  • where curves differ is crucial.
  • Existing methods like Johnson-Neyman (ANCOVA) and Miyazaki-Maier (HLM) have limitations.

Purpose of the Study:

  • To propose novel solutions for determining significance regions in generalized linear (mixed) models (GLM/GLMM).
  • To address limitations of current procedures, including handling non-normally distributed data and biased results.

Main Methods:

  • Developing new test statistics for significance region determination in GLM/GLMM.
  • Incorporating Scheffé's method to control Type I error rates.
  • Ensuring a single statistical software package can be used for analysis.

Main Results:

  • The proposed solutions effectively determine significance regions for GLM/GLMM.
  • The new methods overcome the bias issues associated with the Wald test in the M-M procedure.
  • Type I error rates are controlled, and analyses can be performed within a single software package.

Conclusions:

  • The proposed methods offer a robust and accurate approach to identifying significance regions in GLM/GLMM.
  • These solutions are suitable for non-normally distributed data, a key limitation of prior techniques.
  • The integrated approach simplifies the process for researchers.