Related Experiment Video
Updated: Jun 25, 2025
08:12
A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
Published on: March 1, 2022
2.5K
Likelihood Ratio Test and the Evidential Approach for 2 × 2 Tables
1Department of Pharmacology & Biostatistics, College of Medicine, Alfaisal University, Riyadh 11533, Saudi Arabia.
Entropy (Basel, Switzerland)
|May 24, 2024
Summary
The likelihood ratio test (LRT) is recommended over the chi-squared (χ2) test for analyzing 2 × 2 contingency tables when testing binomial proportions. The χ2 test is better suited for assessing data integrity and low variance scenarios.
Area of Science:
- Statistics
- Biostatistics
- Medical Research
Background:
- Categorical data analysis using 2 × 2 contingency tables is prevalent in medical research.
- Commonly used statistics include risk difference, risk ratio, odds ratio, and log odds.
- Both chi-squared (χ2) tests and likelihood ratio tests (LRT) are employed for analysis.
Purpose of the Study:
- To determine the appropriate statistical test for analyzing 2 × 2 contingency tables.
- To evaluate the suitability of the χ2 test versus the LRT for specific research questions.
- To advocate for the use of the LRT for testing binomial proportions and an evidential approach for data integrity.
Main Methods:
- Literature review.
- Examination of theoretical foundations.
- Analysis of simulation and empirical data.
Main Results:
- The likelihood ratio test (LRT) is the preferred method for testing the equality of binomial proportions.
- The chi-squared (χ2) test is often misused for this purpose.
- The χ2 test is appropriate for scenarios where low variance or data integrity is of interest.
Conclusions:
- The LRT provides a more consistent and coherent approach for testing binomial proportions.
- An evidential approach using log likelihood ratios is recommended for flexibility in testing proportions or variance.
- Findings are applicable to larger and multi-way contingency tables.
Related Concept Videos
01:21Introduction to Test of Independence
2.2K
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:
The test statistic for a test of independence is similar to that of a goodness-of-fit test:
2.2K
01:29Contingency Table
2.5K
A contingency table provides a way of portraying data that can facilitate calculating probabilities. It is a method of displaying a frequency distribution as a table with rows and columns to show how two variables may be dependent (contingent) upon each other; The table helps determine conditional probabilities quite quickly and can help systematically organize, analyze and quantify data. The table displays sample values concerning two variables that may be dependent or contingent on one...
2.5K
01:16Hypothesis Test for Test of Independence
3.6K
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)...
H0: The two variables (factors)...
3.6K
01:08Determination of Expected Frequency
2.2K
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...
2.2K
01:19Expected Frequencies in Goodness-of-Fit Tests
2.5K
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).
2.5K
01:08Fisher's Exact Test
471
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...
471