From 5568dd24af18b1c17802037085bff8591ecac784 Mon Sep 17 00:00:00 2001
From: SamCH93 <samuel.pawel@gmail.com>
Date: Tue, 11 Apr 2023 10:58:58 +0200
Subject: [PATCH] change Table to Box

---
 paper/rsabsence.Rnw | 123 +++++++++++++++++++++++---------------------
 rsabsence.pdf       | Bin 303621 -> 304284 bytes
 2 files changed, 65 insertions(+), 58 deletions(-)
 mode change 100644 => 100755 rsabsence.pdf

diff --git a/paper/rsabsence.Rnw b/paper/rsabsence.Rnw
index 556f149..9944c13 100755
--- a/paper/rsabsence.Rnw
+++ b/paper/rsabsence.Rnw
@@ -8,10 +8,14 @@
 \usepackage{doi}
 \usetikzlibrary{decorations.pathreplacing,calligraphy} % for tikz curly braces
 \usepackage{todonotes}
+\usepackage{nameref}
+\usepackage{caption}
 
 \definecolor{darkblue2}{HTML}{273B81}
 \definecolor{darkred2}{HTML}{D92102}
 
+\fboxsep=20pt % for Box
+
 \title{Replication of ``null results'' -- Absence of evidence or evidence of
   absence?}
 
@@ -861,68 +865,71 @@ or absence of an effect. It seems logically questionable to declare an
 inconclusive replication of an inconclusive original study as a replication
 success. While it is important to replicate original studies with null results,
 our analysis highlights that they should be analyzed and interpreted
-appropriately. Table~\ref{tab:recommendations} summarizes our recommendations.
+appropriately. Box~\hyperref[box:recommendations]{1} summarizes our
+recommendations.
 
-\begin{table}[!htb]
+\begin{table}[!h]
   \centering
-  \caption{Recommendations for the analysis of replication studies of original
-    null results. Calculations are based on effect estimates $\hat{\theta}_{i}$
-    with standard errors $\sigma_{i}$ for $i \in \{o, r\}$ from an original
-    study (subscript $o$) and its replication (subscript $r$). Both effect
-    estimates are assumed to be normally distributed around the true effect size
-    $\theta$ with known variance $\sigma^{2}$. The effect size $\theta_{n}$
-    represents the value of no effect, typically $\theta_{n} = 0$.}
-  \label{tab:recommendations}
-  \begin{tabular}{p{0.95\textwidth}}
-    \toprule
-    \textbf{Equivalence test}
-    \begin{enumerate}
-      \item Specify a margin $\Delta > 0$ that defines an equivalence range
-      $[\theta_{n} - \Delta, \theta_{n} + \Delta]$ in which effects are
-      considered absent for practical purposes.
-      \item Compute the TOST $p$-values for original and replication data
-            $$p_{\text{TOST}i}
-            = \max\left\{\Phi\left(\frac{\hat{\theta}_{i} - \theta_{n} - \Delta}{\sigma_{i}}\right),
+  \caption*{Box 1: Recommendations for the analysis of replication studies of
+    original null results. Calculations are based on effect estimates
+    $\hat{\theta}_{i}$ with standard errors $\sigma_{i}$ for $i \in \{o, r\}$
+    from an original study (subscript $o$) and its replication (subscript $r$).
+    Both effect estimates are assumed to be normally distributed around the true
+    effect size $\theta$ with known variance $\sigma^{2}$. The effect size
+    $\theta_{n}$ represents the value of no effect, typically $\theta_{n} = 0$.}
+  \label{box:recommendations}
+  \fbox{
+    \begin{tabular}{p{0.875\textwidth}}
+      % \toprule
+      \textbf{Equivalence test}
+      \begin{enumerate}
+        \item Specify a margin $\Delta > 0$ that defines an equivalence range
+              $[\theta_{n} - \Delta, \theta_{n} + \Delta]$ in which effects are
+              considered absent for practical purposes.
+        \item Compute the TOST $p$-values for original and replication data
+              $$p_{\text{TOST}i}
+              = \max\left\{\Phi\left(\frac{\hat{\theta}_{i} - \theta_{n} - \Delta}{\sigma_{i}}\right),
               1 - \Phi\left(\frac{\hat{\theta}_{i} - \theta_{n} + \Delta}{\sigma_{i}}\right)\right\},
-            ~ i \in \{o, r\}$$
-            with $\Phi(\cdot)$ the cumulative distribution function of the
-            standard normal distribution.
-      \item Declare replication success at level $\alpha$ if
-            $p_{\text{TOST}o} \leq \alpha$ and $p_{\text{TOST}r} \leq \alpha$,
-            conventionally $\alpha = 0.05$.
-      \item Perform a sensitivity analysis with respect to the margin $\Delta$.
-            For example, visualize the TOST $p$-values for different margins to
-            assess the robustness of the conclusions.
-    \end{enumerate} \\
-    \midrule \textbf{Bayes factor}
-    \begin{enumerate}
-      \item Specify a prior distribution for the effect size $\theta$ that
-            represents plausible values under the alternative hypothesis that
-            there is an effect ($H_{1}\colon \theta \neq \theta_{n})$. For
-            example, specify the mean $m$ and variance $v$ of a normal
-            distribution $\theta \given H_{1} \sim \Nor(m ,v)$.
-      \item Compute the Bayes factors contrasting
-            $H_{0} \colon \theta = \theta_{n}$ to
-            $H_{1} \colon \theta \neq \theta_{n}$ for original and replication
-            data. Assuming a normal prior distribution,
-            % $\theta \given H_{1} \sim \Nor(m ,v)$,
-            the Bayes factor is
-            $$\BF_{01i}
-            = \sqrt{1 + \frac{v}{\sigma^{2}_{i}}} \, \exp\left[-\frac{1}{2} \left\{\frac{(\hat{\theta}_{i} -
-                  \theta_{n})^{2}}{\sigma^{2}_{i}} - \frac{(\hat{\theta}_{i} - m)^{2}}{\sigma^{2}_{i} + v}
+              ~ i \in \{o, r\}$$
+              with $\Phi(\cdot)$ the cumulative distribution function of the
+              standard normal distribution.
+        \item Declare replication success at level $\alpha$ if
+              $p_{\text{TOST}o} \leq \alpha$ and $p_{\text{TOST}r} \leq \alpha$,
+              conventionally $\alpha = 0.05$.
+        \item Perform a sensitivity analysis with respect to the margin $\Delta$.
+              For example, visualize the TOST $p$-values for different margins to
+              assess the robustness of the conclusions.
+      \end{enumerate} \\
+      % \midrule
+      \textbf{Bayes factor}
+      \begin{enumerate}
+        \item Specify a prior distribution for the effect size $\theta$ that
+              represents plausible values under the alternative hypothesis that
+              there is an effect ($H_{1}\colon \theta \neq \theta_{n})$. For
+              example, specify the mean $m$ and variance $v$ of a normal
+              distribution $\theta \given H_{1} \sim \Nor(m ,v)$.
+        \item Compute the Bayes factors contrasting
+              $H_{0} \colon \theta = \theta_{n}$ to
+              $H_{1} \colon \theta \neq \theta_{n}$ for original and replication
+              data. Assuming a normal prior distribution,
+              % $\theta \given H_{1} \sim \Nor(m ,v)$,
+              the Bayes factor is
+              $$\BF_{01i}
+              = \sqrt{1 + \frac{v}{\sigma^{2}_{i}}} \, \exp\left[-\frac{1}{2} \left\{\frac{(\hat{\theta}_{i} -
+              \theta_{n})^{2}}{\sigma^{2}_{i}} - \frac{(\hat{\theta}_{i} - m)^{2}}{\sigma^{2}_{i} + v}
               \right\}\right], ~ i \in \{o, r\}.$$
-      \item Declare replication success at level $\gamma > 1$ if
-            $\BF_{01o} \geq \gamma$ and $\BF_{01r} \geq \gamma$, conventionally
-            $\gamma = 3$ (substantial evidence) or $\gamma = 10$ (strong
-            evidence).
-      \item Perform a sensitivity analysis with respect to the prior
-            distribution. For example, visualize the Bayes factors for different
-            prior standard deviations to assess the robustness of the
-            conclusions.
-    \end{enumerate}
-    \\
-    \bottomrule
-  \end{tabular}
+        \item Declare replication success at level $\gamma > 1$ if
+              $\BF_{01o} \geq \gamma$ and $\BF_{01r} \geq \gamma$, conventionally
+              $\gamma = 3$ (substantial evidence) or $\gamma = 10$ (strong
+              evidence).
+        \item Perform a sensitivity analysis with respect to the prior
+              distribution. For example, visualize the Bayes factors for different
+              prior standard deviations to assess the robustness of the
+              conclusions.
+      \end{enumerate}
+      % \\ \bottomrule
+    \end{tabular}
+  }
 \end{table}
 
 For both the equivalence testing and the Bayes factor approach, it is critical
diff --git a/rsabsence.pdf b/rsabsence.pdf
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