Evidential paradigm	Frequentist paradigm
Evidence for two simple hypothesized values of θ	$\text{Observed}\text{LR},\frac{L_{\mathrm{o}\mathrm{b}\mathrm{s}}({\theta }_1)}{L_{\mathrm{o}\mathrm{b}\mathrm{s}}({\theta }_0)}$	${P‐\text{value}=P}_0\left\{\frac{L({\theta }_1)}{L({\theta }_0)}\ge \frac{L_{\mathrm{o}\mathrm{b}\mathrm{s}}({\theta }_1)}{L_{\mathrm{o}\mathrm{b}\mathrm{s}}({\theta }_0)}\right\}$
Error favoring ${\theta }_1$ when ${\theta }_0$ is true	$M_0(n,k)=P_0\left\{\frac{L({\theta }_1)}{L({\theta }_0)}\ge k\right\}\le \frac{1}{k}\forall n$	$\alpha =P_0\left\{\frac{L({\theta }_1)}{L({\theta }_0)}\ge c\right\}$
Strong evidence	$\frac{L_{\mathrm{o}\mathrm{b}\mathrm{s}}({\theta }_1)}{L_{\mathrm{o}\mathrm{b}\mathrm{s}}({\theta }_0)}\ge k$	$\begin{array}{c}p\le \alpha \\ \iff \\ \frac{L_{\mathrm{o}\mathrm{b}\mathrm{s}}({\theta }_1)}{L_{\mathrm{o}\mathrm{b}\mathrm{s}}({\theta }_0)}\ge c_{a,n}\end{array}$
Intervalsa (e.g., mean of a normal distribution)	$\begin{array}{c}1/k\text{Likelihood}\mathrm{I}\text{nterval}\\ \overline{x}\pm \sqrt{2\log k}\sigma /\sqrt{n}\\ \frac{1}{8}\text{LI}\iff 95.9\%\text{CI}\end{array}$	$\begin{array}{c}(1-\alpha )100\%\text{Exact}\mathrm{C}\text{onfidence}\mathrm{I}\text{nterval}\\ \overline{x}\pm Z_{\alpha /2}\sigma /\sqrt{n}\\ 95\%\text{CI}\iff \frac{1}{6.67}\text{LI}\end{array}$
Other errors to minimize for study planning	$\begin{array}{c}{M}_1(n,k)=P_1\left\{\frac{L({\theta }_1)}{L({\theta }_0)}\le \frac{1}{k}\right\}\\ W_1(n,k)=P_1\left\{\frac{1}{k}<\frac{L({\theta }_1)}{L({\theta }_0)}<k\right\}\\ W_0(n,k)=P_0\left\{\frac{1}{k}<\frac{L({\theta }_1)}{L({\theta }_0)}<k\right\}\end{array}$	$\begin{array}{c}\mathrm{T}\mathrm{y}\mathrm{p}\mathrm{e}\mathrm{I}\mathrm{I}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}\\ \beta =P_1\left\{\frac{L({\theta }_1)}{L({\theta }_0)}\le c_{a,n}\right\}\end{array}$ b
Relationships	Strong evidence, k, and error $M_0(n,k)$ are decoupled	Strong evidence, $p\le \alpha$ and error $\alpha$ are coupled
aThere is a relationship, beyond the normal distribution, between exact confidence intervals and likelihood intervals but confidence intervals are also coupled with the Type I error probability.
bThe Type II error, β, is analogous to M 1(n, k) + W 1(n, k) but for fixed α, n. Power (1 − β) is defined for a fixed α, therefore, although similar in spirit, is always greater than the probability of strong evidence at conventional Type I error levels and therefore the two represent different quantities. There is no concept of controlling weak evidence in the Frequentist paradigm.