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Related Concept Videos

Introduction to Test of Independence01:21

Introduction to Test of Independence

In statistics, the term independence means that one can directly obtain the probability of any event involving both variables by multiplying their individual probabilities. Tests of independence are chi-square tests involving the use of a contingency table of observed (data) values.
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
Hypothesis Test for Test of Independence01:16

Hypothesis Test for Test of Independence

The test of independence is a chi-square-based test used to determine whether two variables or factors are independent or dependent. This hypothesis test is used to examine the independence of the variables. One can construct two qualitative survey questions or experiments based on the variables in a contingency table. The goal is to see if the two variables are unrelated (independent) or related (dependent). The null and alternative hypotheses for this test are:
H0: The two variables (factors)...
Test for Homogeneity01:23

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...
Determination of Expected Frequency01:08

Determination of Expected Frequency

Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
Comparing the Survival Analysis of Two or More Groups01:20

Comparing the Survival Analysis of Two or More Groups

Survival analysis is a cornerstone of medical research, used to evaluate the time until an event of interest occurs, such as death, disease recurrence, or recovery. Unlike standard statistical methods, survival analysis is particularly adept at handling censored data—instances where the event has not occurred for some participants by the end of the study or remains unobserved. To address these unique challenges, specialized techniques like the Kaplan-Meier estimator, log-rank test, and Cox...
Fisher's Exact Test01:08

Fisher's Exact Test

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 the...

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Related Experiment Video

Updated: Jul 14, 2026

An R-Based Landscape Validation of a Competing Risk Model
05:37

An R-Based Landscape Validation of a Competing Risk Model

Published on: September 16, 2022

Comparing two independent incidence rates using conditional and unconditional exact tests.

Cong Han1

  • 1TAP Pharmaceutical Products, Inc., Lake Forest, IL 6004, USA. cong.han@tap.com

Pharmaceutical Statistics
|May 17, 2007
PubMed
Summary

New exact tests for comparing two independent Poisson rates offer improved power. Unconditional exact tests using binomial p-value, likelihood ratio, or efficient score are recommended over Wald statistics for better statistical power.

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Establishing a Competing Risk Regression Nomogram Model for Survival Data
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Last Updated: Jul 14, 2026

An R-Based Landscape Validation of a Competing Risk Model
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Published on: September 16, 2022

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04:57

Establishing a Competing Risk Regression Nomogram Model for Survival Data

Published on: October 23, 2020

Area of Science:

  • Biostatistics
  • Statistical Inference
  • Clinical Trials

Background:

  • Accurate comparison of independent Poisson rates is crucial in medical research, particularly in cardiovascular trials.
  • Existing conditional exact tests may lack sufficient statistical power in certain scenarios.
  • Controlling Type I error rates at the nominal level is a primary requirement for valid statistical tests.

Purpose of the Study:

  • To propose and evaluate novel unconditional exact tests for comparing two independent Poisson rates.
  • To compare the power and performance of these new tests against the traditional conditional exact test.
  • To provide recommendations for the most effective statistical methods for Poisson rate comparisons.

Main Methods:

  • Development of several unconditional exact tests utilizing different test statistics (binomial p-value, likelihood ratio, efficient score, Wald statistics).
  • Comparison of proposed tests with the conditional exact test based on a binomial distribution.
  • Evaluation of Type I error control and statistical power across various scenarios.

Main Results:

  • Unconditional exact tests employing binomial p-value, likelihood ratio, or efficient score demonstrated improved statistical power compared to the conditional exact test.
  • Unconditional exact tests using Wald statistics (original or square-root scale) were found to be substantially less powerful.
  • The proposed unconditional exact tests effectively control Type I error rates at the nominal level.

Conclusions:

  • Unconditional exact tests using binomial p-value, likelihood ratio, or efficient score are recommended for comparing two independent Poisson rates due to enhanced power.
  • Unconditional exact tests based on Wald statistics are not recommended for this purpose.
  • The findings are illustrated with a practical example from a cardiovascular trial, highlighting the clinical relevance.