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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.