Content deleted Content added
Line 17:
===Approximation===
If the distribution of the likelihood ratio corresponding to a particular null and alternative hypothesis can be explicitly determined then it can directly be used to form decision regions (to accept/reject the null hypothesis). In most cases, however, the exact distribution of the likelihood ratio corresponding to specific hypotheses is very difficult to determine. A convenient result, though, says that as the sample size <math>n</math> approaches <math>\infty</math>, the test statistic <math>-2 \log(\Lambda)</math> will be asymptotically [[chi-squared distribution|<math>\chi^2</math> distributed]] with [[degrees of freedom (statistics)|degrees of freedom]] equal to the difference in dimensionality of <math>\Theta</math> and <math>\Theta_0</math>. This means that for a great variety of hypothesis, a practitioner can take the likelihood ratio <math>\Lambda</math>, algebraically manipulate <math>\Lambda</math> into <math>-2\log(\Lambda)</math>, compare the value of <math>-2\log(\Lambda)</math> given a particular result to the chi squared value corresponding to a desired statistical significance, and create a reasonable decision based on that comparison.
== Examples ==
| |||