Likelihood Ratio Calculator

Formula

To calculate the Likelihood Ratio (LR):

\[ LR = \frac{L_{alt}}{L_{null}} \]

Where:

\(LR\) is the Likelihood Ratio
\(L_{alt}\) is the likelihood of the alternative hypothesis
\(L_{null}\) is the likelihood of the null hypothesis

What is the Likelihood Ratio?

The Likelihood Ratio (LR) is a measure used in statistical hypothesis testing to compare the fit of two models: the null hypothesis and the alternative hypothesis. It is calculated by dividing the likelihood of the alternative hypothesis by the likelihood of the null hypothesis. A higher LR indicates that the alternative hypothesis is more likely given the data.

Example Calculation 1

Let's assume the following values:

Null Hypothesis Likelihood (\(L_{null}\)) = 0.2
Alternative Hypothesis Likelihood (\(L_{alt}\)) = 0.5

Using the formula:

\[ LR = \frac{0.5}{0.2} = 2.5 \]

The Likelihood Ratio is 2.5.

Example Calculation 2

Let's assume the following values:

Null Hypothesis Likelihood (\(L_{null}\)) = 0.1
Alternative Hypothesis Likelihood (\(L_{alt}\)) = 0.3

Using the formula:

\[ LR = \frac{0.3}{0.1} = 3 \]

The Likelihood Ratio is 3.