Construct Validity of the Tower of London Test: Generating a Construct Specification Equation Relating Problem Characteristics to Problem Difficulty in a Sample of Veterans with Mild Traumatic Brain Injury

The Tower of London (TOL) is a set of problem-solving tasks that are commonly used to measure cognition. No studies have developed construct specification equations (CSEs) to mathematically quantify how the characteristics of test problems relate to the difficulty of the problem in the TOL. We aimed to investigate the relationship between TOL problem characteristics and problem difficulty in Veterans with mild traumatic brain injury (mTBI). For each problem, the sample average of moves, time, and optimal moves was used to quantify TOL problem difficulty from 77 Veterans with mild traumatic brain injury. Problem characteristics of minimum moves, optimal paths, move choices, start position, and goal position for 29 TOL problems were linearly regressed against quantifications of TOL problem difficulty. Only the problem characteristic of minimum moves showed a significant correlation across all three quantifications of problem difficulty (<i>r</i> = |-.460|-.851). Minimum moves accounted for 71.4 % and 51.2% of the adjusted variance of problem difficulty quantified by average moves and average time, respectively. A CSE depicting the relationship of the TOL problem characteristics of minimum moves to problem difficulty, as measured by average moves, was highly accurate. These findings have implications for selecting primary TOL performance variables for research studies and provide insight into creating shorter TOL versions.