# The Effectiveness of Unimodal and Multimodal Warnings on Drivers' Response Time: A Meta-Analysis
## 2 Method
### Statistical Analysis Strategies  
[PERSON]'s _d_[90], a common format of standardized mean difference (SMD), is used as the summary indicator when processing continuous result data; however, this conclusive method showed a slight deviation in small-scale studies. Therefore, the effect size of the current meta-analysis was measured using Hedges' \(g\), which is adjusted for small-sample size bias and visualized using the forest plot [91; 92; 93]. A value of 0.2, 0.5, 0.8 of [PERSON]'s \(d\) and [PERSON] \(g\) represents a small, medium, and large effect size respectively [94]. Weighted random-effects meta regression models and forest plots were generated using the ROBUMETA package in R [95]. We accounted for statistical dependencies in studies that reported multiple effect sizes from the same sample using [PERSON], [PERSON], and [PERSON]'s random effects robust standard error estimate technique [96]. The random-effects robust variance estimation (RVE) methodology is used to attribute the statistical interdependence of various effect sizes from the same sample. By modifying the study standard errors to account for correlations across effect sizes from the same sample, RVE is able to accommodate clustered data. For the calculation of the inter-study sampling variance estimate, the RVE requires an estimate of the mean correlation (\(\rho\)) between all pairs of effect sizes inside a cluster. Following the calculation of the average weighted effect size, a forest plot was drawn to provide the summary effect from the random-effects model, as well as the effect sizes extracted from each individual study, displaying the full distribution of effect sizes that made up the average weighted effect size. The presence and amount of heterogeneity among effect sizes were investigated using the \(I^{2}\) and \(\tau^{2}\) statistics. \(I^{2}\) is the percentage of effect size variation caused by non-sampling errors; and \(\tau^{2}\) is the between-study variance, which is utilized to conduct random effects analysis. This methodology was proposed by [PERSON] to overcome the shortcoming of the Q test (sensitive to the number of studies) [97]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Comparison Category** & **Pairwise Comparison** & **Pooled Hedges\({}^{\prime}\)g (95\% CI)** & **\(\star^{2}\) (Tau.sq)** & **Failsafe-N Estimates** \\ \hline \multirow{3}{*}{Unimodal vs. control condition} & Visual vs. control & 0.83 (\(-\)0.50, 2.16) & 0.85 & 440 \\ \cline{2-5}  & Auditory vs. control & 0.98 ** (0.34, 1.61) & 0.88 & 344 \\ \cline{2-5}  & Tactile vs. control & 0.77 ** (0.22, 1.32)** & 0.72 & 518 \\ \hline \multirow{3}{*}{Unimodal vs. unimodal} & Visual vs. tactile & 0.74 ** (0.11, 1.37)** & 0.92 & 468 \\ \cline{2-5}  & Auditory vs. tactile & 0.11 (\(-\)0.40, 0.61) & 0.71 & 64 \\ \cline{2-5}  & Visual vs. auditory & 0.42 (\(-\)0.12, 0.97) & 1.18 & 141 \\ \hline \multirow{3}{*}{Unimodal vs. bimodal} & Auditory vs. auditory-tactile & 0.38 ** (0.04, 0.72)** & 0.20 & 211 \\ \cline{2-5}  & Tactile vs. auditory-tactile & 0.46 ** (0.10, 0.82)** & 0.21 & 268 \\ \cline{2-5}  & Auditory vs. visual-auditory & 0.37 (\(-\)0.34, 1.08) & 0.64 & 189 \\ \cline{2-5}  & Tactile vs. visual-auditory & 0.39 (\(-\)0.22, 1.00) & 0.22 & 144 \\ \cline{2-5}  & Auditory vs. visual-tactile & 0.38 (\(-\)0.60, 1.36) & 0.44 & 149 \\ \cline{2-5}  & Tactile vs. visual-tactile & 0.36 (\(-\)0.04, 0.76) & 0.12 & 153 \\ \hline \multirow{3}{*}{Bimodal vs. trimodal} & visual-auditory vs. visual-auditory-tactile & 0.54 (\(-\)0.49, 1.57) & 0.48 & 67 \\ \cline{2-5}  & visual-tactile vs. visual-auditory-tactile & 0.40 (\(-\)0.29, 1.00) & 0.21 & 41 \\ \cline{1-1} \cline{2-5}  & auditory-tactile vs. visual-auditory-tactile & 0.26 (\(-\)0.25, 0.77) & 0.12 & 95 \\ \hline \hline \end{tabular} Note. A single asterisk represents significance at \(\rho<0.05\); Double asterisks represent significance at \(\rho<0.01\).  
\end{table} 
Table 2: Pooled Hedges \(g\) and 95% CI of Pairwise Comparisons of Warning Modalities.