Inference via likelihood

The likelihood school affirms that likelihood ratios are the basic tool of inference. The likelihood is the (conjugate) probability of observed data D, conditional on the hypothesis A being true.

    \[L = Pr(D|A)\]

Given two hypotheses, A and B, it is meaningless to assess evidence except by comparing the evidence favoring hypothesis A over hypothesis B. According to the law of likelihood, the degree to which the evidence supports one hypothesis over the other is the ratio of the two probabilities, or likelihood ratio (LR), which ultimately reduces to


Odds ratios (OR) have a similar form because odds ratios are ratios of the likelihood of the occurrence of an event versus its non-occurrence.

A LR is a tool for quantifying the strength of evidence, while NHSTs are decision procedures. The LR ranges from zero to infinity, with 1 being equipoise, and values above 32 arbitrarily defined as strong evidence, and values over 8 as medium strong evidence.

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