## 3 Results (Study 1)
### Phase 2: Classification and Ranking of the FOD--A Combinations Based upon Simulator Performance  
The results from Phase 1 revealed mean differences on seven simulator performance variables. Two of these significant variables (variability of speed and number of distractor E presses) were removed from the further analyses since both had no variability (i.e., were constant) for at least one FOD-A combination. Variability of speed was zero in combination 1 since the cruise control was enabled and the number of distractor E presses were not used in combination 1 and combination 2 (see Table 3). The five remaining significant simulator variables are: average target E reaction time, average brake reaction time, average speed, percent of target Es detected, and number of target E extra presses. With the goal of rank-ordering the FOD-A combinations, these five significant simulator variables were used in a linear discriminant analysis [46]. The discriminant analysis was statistically significant, [PERSON]'s \(\Lambda\) = 0.08, \(\chi^{2}\)(15) = 348.23, \(p\) < 0.001, meaning that the discriminant function can classify the FOD-A combinations using these five significant simulator variables. The discriminant function was written as an equation containing a weight associated with each variable indicating the variable's contribution to distinguishing the different groups. The magnitude of the weight is quantified as the distance from the zero (i.e., using the absolute value). Specifically, the larger the absolute magnitude of the weight, the larger the contribution to discriminating among the FOD-A combinations. In Equation (1), the largest weight of 1.59 was associated with average target E reaction time. This suggests that among the five simulator performance variables average target E reaction time makes the largest contribution towards distinguishing among the combinations. The first discriminant function, or first linear combination, is shown below to demonstrate the calculation of the discriminant score using all five variables with their corresponding weights:  
\[\mathrm{D=}(-1.59)Z_{1}+(-0.87)Z_{2}+(0.30)Z_{3}+(0.13)Z_{4}+(-0.08)Z_{5} \tag{1}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Significant Variables** & **ANOVA Result** & **Summary** \\ \hline Average brake reaction time (s) & 1.0 & \(F\)(3,30) = 35.648, \(p\) < 0.001. The effect size (\(\eta^{2}\) = 0.448) indicates 44.8% of the variance in the average reaction time to apply the brake was due to different combination selections. & The increase in workload in combination 2, 3, and 4 likely caused the increase in the brake response time. \\ \hline Average speed (mph) & 20 & \(F\)(3,30) = 11.848, \(p\) < 0.001. The effect size (\(\eta^{2}\) = 0.212) indicates 21.2% of the variance in average speed was due to different combination selection. & In comparison to using cruise control (combination 1), combination 2, 3, and 4 were significantly slower. Combination 2, 3 and 4 were not meaningfully different from one another. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: _Cont._where D = Discriminant score, \(Z_{1}=\) Average target E reaction time, \(Z_{2}=\) Percent of target Es detected, \(Z_{3}=\) Average brake reaction time, \(Z_{4}=\) Number of target E extra presses, and \(Z_{5}=\) Average speed. The first discriminant function explained 92.34% of the variance in the linear combination of the five simulator variables. The results of the first discriminant function indicated that variables can be rank ordered in terms of their ability to discriminate among the four FOD-A combinations as follows: average target E reaction time (1.59), percent of target Es detected (0.87), average brake reaction time (0.30), number of target E extra presses (0.13), and average speed (0.08).