# 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
### Motor Tasks  
In order to evaluate the information based processing time in case of motor task with low cognitive content (T\({}_{\text{p,m}}\)), experimental test data from to two previous researches have been considered [57; 58]. Data are obtained by the Purdue Pegboard Test (PPT); they refer to individuals with different age with a total of 437 subjects (219 females and 218 males). The first study [57] provides data referring to people aged from 15 to 40 years old; the second study [58] focuses on people aged from 40 to 89 years old. Data available from the literature are used to evaluate the correlations between age and movement \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**} \\
**Sex** & **M** & **F** & **M** & **F** & **M** & **F** \\ \hline T\({}_{\text{p,c}}\)-SC (ms/bit) & 190.7 & 191.8 & 191.6 & 198.9 & 197.9 & 204.7 \\ T\({}_{\text{p,c}}\)-MC (ms/bit) & 187.8 & 188.5 & 177.5 & 180.9 & 201.1 & 202.0 \\ Average T\({}_{\text{p,c}}\) (ms/bit) & 189.3 & 190.1 & 184.5 & 189.9 & 199.5 & 203.3 \\ \hline
**Age Class** & \multicolumn{2}{c}{**44**} & \multicolumn{2}{c}{**56**} & \multicolumn{2}{c}{**63**} \\
**Sex** & **M** & **F** & **M** & **F** & **M** & **F** \\ \hline T\({}_{\text{p,c}}\)-SC (ms/bit) & 205.5 & 216.3 & 226.3 & 224.6 & 242.8 & 243.8 \\ T\({}_{\text{p,c}}\)-MC (ms/bit) & 208.8 & 204.8 & 234.4 & 233.4 & 240.2 & 238.9 \\ Average T\({}_{\text{p,c}}\) (ms/bit) & 207.2 & 210.6 & 230.3 & 229.0 & 241.5 & 241.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cognitive processing time T\({}_{\text{p,c}}\) (s, A) in single-choice (SC) and multiple-choice (MC) tests (M for male, F for female) derived from Equation (9) on the basis of data from [54]. Figure 3: T\({}_{\text{p,c}}\) values vs. age and sex from Equation (9) on the basis of data from [54]. time by an information-based approach. An information-based model evaluating the information volume to be processed to accomplish a motor task is proposed. The related motor processing time (T\({}_{\text{p,m}}\)) required by an individual of a specific class of age and sex to accomplish a motor task with low cognitive content is evaluated. The time to perform the task in the PPT is the movement time (MT) of 30 s during each test run. Only data related to the preferred hand of the subjects are considered (so to not influence the performance with the different manual dexterity of the hands). Under these hypotheses, Equation (7) is considered to evaluate the motor processing time for a given sex and age (T\({}_{\text{p,m}}\) (s, A)) as:  
\[\text{T}_{\text{p,m}}(\text{s},\text{A})=\frac{\text{MT}(\text{I}_{\text{m}},\text{s},\text{A})}{\text{I}_{\text{m}}}\ \bigg{[}\frac{\text{s}}{\text{bit}}\bigg{]}. \tag{12}\]  
Consistently, the information processing rate of population of sex s and age class A, can be obtained as:  
\[\text{IPR}_{\text{m}}(\text{s},\text{A})=\frac{1}{\text{T}_{\text{p,m}}(\text{ s},\text{A})}\ \bigg{[}\frac{\text{bit}}{\text{s}}\bigg{]}. \tag{13}\]  
In order to evaluate the motor processing time (T\({}_{\text{p,m}}\) (s, A)) from data provided by the PPT, the I\({}_{\text{m,MTM}}\) (Equation (8b)) has to be calculated. MTM standard provides average standard time not distinguishing age and sex. As a consequence, an average information volume corresponding to MTM standard times can be calculated by means of Equation (8b) where an average (on age and sex) value of the motor processing time (T\({}_{\text{p,m}}^{*}\)) is considered. In order to evaluate this value (T\({}_{\text{p,m}}^{*}\)), an iterative procedure has been adopted. At the first iteration, T\({}_{\text{p,m}}^{*}\) is assumed equal to 250 ms/bit (named T\({}_{\text{p,m,0}}^{*}\)).