A<unk>  is a statistical test in which a<unk>  is computed between the maximum  probability of a result under two different hypotheses, so that statisticians can make a decision between two hypotheses based on the value of this<unk> .
The numerator corresponds to the maximum probability of an observed result under the null hypothesis. The denominator corresponds to the maximum probability of an observed result under the alternative hypothesis. Under certain regularity conditions, the numerator of this<unk>  is less than the denominator.  The<unk><unk>  under those conditions is between 0 and 1.  Lower values of the<unk><unk>  mean that the observed result was less likely to occur under the null hypothesis.  Higher values mean that the observed result was more likely to occur under the null hypothesis.
The<unk><unk> , denoted as 
Λ
{\displaystyle \Lambda }
 (the Greek letter lambda), is a random variable with a probability distribution.  If the distribution of the<unk><unk>  corresponding to a particular null and alternative hypothesis can be explicitly determined that, directly, can be used to form decision regions to reject or not reject the null hypothesis.
In most cases, however, the exact distribution of the<unk><unk>  corresponding to specific hypotheses is very difficult to determine.  A convenient result, though, says that under certain regularity conditions the distribution of 
−
2
log
⁡
(
Λ
)
{\displaystyle -2\log(\Lambda )}
 will tend to be a chi squared distribution for large sized samples.  Meaning that for a great variety of hypothesis, a practitioner can take the<unk><unk>  
Λ
{\displaystyle \Lambda }
, algebraically manipulate 
Λ
{\displaystyle \Lambda }
 into 
−
2
log
⁡
(
Λ
)
{\displaystyle -2\log(\Lambda )}
, compare the value of 
−
2
log
⁡
(
Λ
)
{\displaystyle -2\log(\Lambda )}
 given a particular result to the chi squared value corresponding to a desired statistical significance, and create a reasonable decision based on that comparison.
Likelihood-ratio test
Chi-square test
Analysis of covariance
Analysis of variance
Kendall tau rank correlation coefficient
Binomial test
Brown-Forsythe test
Shapiro-Wilk test