Statistics & probability

Nested-model likelihood ratio test calculator

Compare nested maximum-likelihood models using the chi-square approximation.

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Behind the numbers

How this calculation works

Compare nested maximum-likelihood models using the chi-square approximation.

THE FORMULAG²=2(ln L_full−ln L_restricted)

A worked example

Log likelihoods −105 and −100 give G²=10 and a p-value near 0.00674 for 2 degrees of freedom.

Good to know

Boundary parameters and small samples can invalidate the chi-square reference.

Read the result

Compare nested maximum-likelihood models using the chi-square approximation.

The primary result is labeled “Likelihood ratio statistic”. Keep the input definitions in view when comparing this result with another method.

Try a related calculation

Boundary parameters and small samples can invalidate the chi-square reference.

For a related exercise, try the statistics calculator.

A few questions, answered

How can I check the default inputs by hand?

Log likelihoods −105 and −100 give G²=10 and a p-value near 0.00674 for 2 degrees of freedom.

Which rule does this calculator apply?

G²=2(ln L_full−ln L_restricted)

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