Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Goodness-of-Fit Test

Goodness-of-Fit Test

The goodness-of-fit test is a type of hypothesis test which determines whether the data "fits" a particular distribution. For example, one may suspect that some anonymous data may fit a binomial distribution. A chi-square test (meaning the distribution for the hypothesis test is chi-square) can be used to determine if there is a fit. The null and alternative hypotheses may be written in sentences or stated as equations or inequalities. The test statistic for a goodness-of-fit test is given as...

Statistical Methods to Analyze Parametric Data: Student t-Test and Goodness-of-Fit Test

Statistical Methods to Analyze Parametric Data: Student t-Test and Goodness-of-Fit Test

In parametric statistics, two fundamental tests stand out for their utility and wide application: the Student's t-test and goodness-of-fit tests. These tests provide researchers with a robust method for drawing insights from data, testing hypotheses, and making informed decisions based on their findings.
The Student's t-test is a statistical test that examines if there is a statistically significant difference between the means of two groups. This test is instrumental when dealing with data...

Expected Frequencies in Goodness-of-Fit Tests

Expected Frequencies in Goodness-of-Fit Tests

A goodness-of-fit test is conducted to determine whether the observed frequency values are statistically similar to the frequencies expected for the dataset. Suppose the expected frequencies for a dataset are equal such as when predicting the frequency of any number appearing when casting a die. In that case, the expected frequency is the ratio of the total number of observations (n) to the number of categories (k).

Bootstrapping

Bootstrapping

The term "bootstrap" originated in the 19th century as a metaphor for self-improvement or achieving something independently, without external assistance. This concept extends to statistical bootstrapping, a self-contained method for estimating population parameters through resampling, even though it can be computationally intensive. Developed by the American statistician Dr. Bradley Efron in 1979, bootstrapping provides a robust way to perform inference when the original sample size is small or...

Test for Homogeneity

Test for Homogeneity

The goodness–of–fit test can be used to decide whether a population fits a given distribution, but it will not suffice to decide whether two populations follow the same unknown distribution. A different test, called the test for homogeneity, can be used to conclude whether two populations have the same distribution. To calculate the test statistic for a test for homogeneity, follow the same procedure as with the test of independence. The hypotheses for the test for homogeneity can be stated as...

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric Survival Analysis: Weibull and Exponential Methods

Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
Weibull Distribution
The Weibull distribution is a flexible model used in parametric survival analysis. It can handle both increasing and decreasing hazard rates, depending on its shape parameter...

You might also read

Related Articles

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

Sort by

Same author

Minimum noninferiority dose for phase I clinical trials with immunotherapy.

Biometrics·2026

Same author

Borrowing information from an unidentifiable model: Guaranteed efficiency gain with a dichotomized outcome in the external data.

Biometrics·2026

Same author

A KL-divergence-based test for elliptical distribution.

Journal of nonparametric statistics·2026

Same author

KAISER CRITERION IN FACTOR MODELS.

Acta mathematica Sinica, English series·2026

Same author

COMMUNITY EXTRACTION OF NETWORK DATA UNDER STOCHASTIC BLOCK MODELS.

Statistica Sinica·2026

Same author

SPARCC: Semi-Parametric Robust Estimation in a Right-Censored Covariate Model.

Journal of the American Statistical Association·2026

Search research articles

Related Experiment Video

Updated: May 11, 2026

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

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

Published on: July 3, 2020

Pearson-type goodness-of-fit test with bootstrap maximum likelihood estimation.

Guosheng Yin¹, Yanyuan Ma

¹Department of Statistics and Actuarial Science The University of Hong Kong Pokfulam Road, Hong Kong gyin@hku.hk.

Electronic Journal of Statistics

|May 31, 2013

Summary

A new bootstrap method modifies the Pearson test statistic to accurately follow a chi-squared distribution. This statistical approach enhances model diagnostics by ensuring reliable test results for data analysis.

Keywords:

Asymptotic distribution bootstrap sample hypothesis testing maximum likelihood estimator model diagnostics

More Related Videos

A Tablet-Based Curriculum-Based Measurement Protocol for Kindergarten Writing

A Tablet-Based Curriculum-Based Measurement Protocol for Kindergarten Writing

Published on: February 7, 2025

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits

Published on: September 27, 2019

Related Experiment Videos

Last Updated: May 11, 2026

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

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

Published on: July 3, 2020

A Tablet-Based Curriculum-Based Measurement Protocol for Kindergarten Writing

A Tablet-Based Curriculum-Based Measurement Protocol for Kindergarten Writing

Published on: February 7, 2025

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits

Published on: September 27, 2019

Area of Science:

Statistics
Statistical Modeling
Data Analysis

Background:

The Pearson test statistic is commonly used for data analysis but often fails to follow a chi-squared distribution when using maximum likelihood estimators (MLE).
This deviation from the expected distribution complicates accurate statistical inference and model assessment.

Purpose of the Study:

To develop a modified Pearson test statistic that reliably follows a chi-squared distribution.
To introduce a bootstrap-based method for improving the accuracy of model diagnostic procedures.

Main Methods:

A bootstrap-based modification of the Pearson test statistic was proposed.
Observed and expected counts were computed using MLE from bootstrap samples.
The proposed method was evaluated for test size and power through simulation studies.

Main Results:

The bootstrap modification successfully recovered the chi-squared distribution for the Pearson test statistic.
The bootstrap-sample MLE introduced the necessary randomness for accurate distribution recovery.
The new bootstrap chi-squared test proved easy to implement.

Conclusions:

The bootstrap-based Pearson test statistic offers a reliable method for model diagnostics.
This approach ensures the test statistic adheres to the chi-squared distribution, facilitating more accurate statistical analysis.
The method is practical and validated through simulations and real-world data application.