# Human Cognitive and Motor Abilities in the Aging Workforce: An Information-Based Model
## 4 An Information-Based Model for Age- and Sex-Dependent Performance Time of Workers
### Cognitive Tasks
Under these hypotheses and by using Equation (5), the processing time of subjects with the same sex (s) and age (A), T\({}_{p,c}\)(s, A), can be evaluated by RT (I\({}_{c}\), s, A), measured in [54] as follows:  
\[\text{T}_{p,c}(\text{s},\text{A})=\frac{\text{RT}(\text{I}_{c},\text{s},\text {A})\times(1-\text{k})}{\text{I}_{c}}\left[\frac{\text{s}}{\text{bit}}\right] \tag{9}\]  
where I\({}_{c}\) is the volume of information of the cognitive task and k is a constant (0.3 \(\leq\) k \(\leq\) 0.4) representing the fraction of the RT due to delays not depending on central processing time (SRT \(=\) k \(\times\) RT). Consistently, the information processing rate of population of given sex and age class in accomplishing a cognitive task, can be obtained as:  
\[\text{IPR}_{\text{c}}(\text{s},\text{A})=\frac{1}{\text{T}_{\text{p},\text{c}}( \text{s},\text{A})}\,\Big{[}\,\frac{\text{bit}}{\text{s}}\,\Big{]}. \tag{10}\]  
In the experiments of [PERSON] and [PERSON] [54], the single-choice RT (SC-RT) and multiple-choice RT (MC-RT) were estimated for both male and female individuals, aged from 16 to 63 years. The mean RT values for different age classes are shown for both sexes and for the single-choice and multiple-choices tests in Table 1.  
When male and female populations are considered altogether, RT values increase linearly with the age class (Figure 2), for single and four-choices test runs, with an increase of about 20-30% from age 24 to 60 +. Also, Higher reaction time values are observed in case of higher information volumes processed (four choices test runs). On the basis of data in [54] and Equation (9) of the model proposed (by assuming k = 0.35), T\({}_{\text{p},\text{c}}\) (s, A) values are computed for both single-choice and multiple-choice tests. Results are in Table 2. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Age Class** & \multicolumn{2}{c}{**16**} & \multicolumn{2}{c}{**24**} & \multicolumn{2}{c}{**36**} \\
**Age Range** & \multicolumn{2}{c}{**15–16**} & \multicolumn{2}{c}{**23–26**} & \multicolumn{2}{c}{**31–41**} \\
**Sex** & **M** & **F** & **M** & **F** & **M** & **F** \\ \hline SC-RT (ms) & 293.4 & 295 & 294.7 & 306 & 304.4 & 314.9 \\ MC-RT (ms) & 577.8 & 580.1 & 546 & 556.5 & 618.9 & 621.5 \\ \hline
**Age Class** & \multicolumn{2}{c}{**44**} & \multicolumn{2}{c}{**56**} & \multicolumn{2}{c}{**63**} \\
**Age Range** & \multicolumn{2}{c}{**39–50**} & \multicolumn{2}{c}{**54–58**} & \multicolumn{2}{c}{**62–66**} \\
**Sex** & **M** & **F** & **M** & **F** & **M** & **F** \\ \hline SC-RT (ms) & 316.2 & 332.8 & 348.1 & 345.6 & 373.5 & 375.1 \\ MC-RT (ms) & 642.5 & 630.3 & 721.2 & 718.1 & 739.1 & 735 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Mean single-choice reaction time (SC-RT) and mean multiple-choice reaction time (MC-RT) for different age classes and sex (M for male, F for female). Source: Authors’ elaboration of data from [54]. Figure 2: Mean reaction time values of the overall population vs. age for single and multiple-choice cognitive tests. Source: Authors’ elaboration of data from [54]. As shown in Figure 3, a linear trend (R\({}^{2}>0.9\)) of T\({}_{\text{p,c}}\) vs. age is observed for male and female; for each age class, sex slightly affects processing time. The linear regression analysis leads to:  
\[\text{T}_{\text{p,c}}(\text{s},\text{A})=\alpha_{\text{c}}(\text{s})+\beta_{ \text{c}}(\text{s})\times\text{A}\left[\frac{\text{s}}{\text{bit}}\right] \tag{11}\]  
where regression parameters \(\alpha_{\text{c}}\) and \(\beta_{\text{c}}\) are in Table 3.  
By (Equation (10)), the information processing rate IPR\({}_{\text{c}}\) (s, A) can be easily evaluated for differently aged male and female subjects.