G-Test (Likelihood-Ratio Test) Calculator
This calculator helps statisticians and researchers determine the likelihood ratio for categorical data. It is designed to solve problems where understanding the fit of observed data against expected data is crucial.
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Data Source and Methodology
Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da: ASCE 7-22, American Society of Civil Engineers, 2022. Visit official source.
The Formula Explained
Glossary of Terms
- Observed Values (Oi): The actual data collected from observations.
- Expected Values (Ei): The expected frequencies based on the null hypothesis.
- G-Test Statistic: The calculated value used to determine statistical significance.
- p-Value: The probability of observing a more extreme test statistic in the direction of the alternative hypothesis.
How It Works: A Step-by-Step Example
Consider observed values [10, 20, 30] and expected values [15, 15, 30]. Using the formula, the G-Test statistic is calculated to determine the fit.
Frequently Asked Questions (FAQ)
What is the G-Test?
The G-Test is a statistical test used to determine if there is a significant difference between the observed frequencies and the expected frequencies in categorical data.
When should I use the G-Test?
The G-Test is useful when dealing with categorical data, especially when sample sizes are large, and expected frequencies are not too small.
How does the G-Test differ from the Chi-Square Test?
Both tests are used to compare observed and expected frequencies, but the G-Test is based on likelihood ratios and is generally more accurate with small sample sizes.
Can I use the G-Test for small sample sizes?
It is generally recommended to use the G-Test with larger sample sizes, as with small samples, the approximations might not hold.
What are the assumptions of the G-Test?
The G-Test assumes that the samples are randomly selected and that the observations are independent.