Inferential Statisticshard
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In a clinical trial, the treatment effect Δ\Delta is assessed via a likelihood ratio test. If the log-likelihood is ℓ(Δ)\ell(\Delta), and we compare a constrained model Δ=0\Delta = 0 to an unconstrained one, what property of the statistic λ=−2[ℓ(0)−ℓ(Δ^)]\lambda = -2[\ell(0) - \ell(\hat{\Delta})] allows us to determine significance without knowing the exact distribution of Δ^\hat{\Delta}?