Likelihood ratio (LR) is a statistical measure used in evaluating hypothesis tests. It is calculated by comparing the likelihood of two hypotheses, one being the null hypothesis and the other being the alternative hypothesis. The LR is the ratio of the likelihood of the data under the alternative hypothesis, and the likelihood of the data under the null hypothesis. The LR is a significant tool in determining the probability of rejecting the null hypothesis in favor of the alternative hypothesis.

The LR is defined as the ratio of the probability of the observed data under the alternative hypothesis to the probability of the observed data under the null hypothesis. The LR is used to determine whether the observed data are more likely to have occurred under the alternative hypothesis or the null hypothesis. If the LR is greater than one, then the data are more likely to have come from the alternative hypothesis. If the LR is less than one, then the data are more likely to have come from the null hypothesis.

The LR can be used to evaluate hypothesis tests in various fields, such as psychology, economics, and medical research. The LR is often used as a measure of the strength of evidence in favor of the alternative hypothesis. It is also used to compare two or more hypotheses, and to determine which hypothesis is more likely to be true.

The LR is also used in the fields of forensic science and biostatistics. In forensic science, the LR is used to compare the likelihood of a suspectâ€™s DNA matching that of a crime scene sample. In biostatistics, the LR is used to evaluate the likelihood of a disease being caused by a particular environmental factor.

The LR is a powerful statistic that can be used to evaluate hypothesis tests in a variety of fields. It is an easy to use and understand measure that can be used to evaluate the strength of evidence in favor of an alternative hypothesis.

References

Bretz, F., Hothorn, T., & Westfall, P. (2011). Multiple comparisons using R. Boca Raton, FL: CRC Press.

Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression (2nd ed.). New York, NY: Wiley.

Kachigan, S. K. (1986). Statistical analysis: An interdisciplinary introduction to univariate & multivariate methods. New York, NY: Radius Press.

Yu, S. (2016). Hypothesis testing using likelihood ratio tests. Retrieved from https://www.stat.berkeley.edu/~stark/Teach/stat210b/Lectures/Lec2.pdf