I have a pretty general question: I'm working on my thesis and I took an online test from some people. I want to assign score to each person based on
- number of their correct answer (C) and
- their average response time (T). My idea for scoring them is to divide number of correct answer by average response time (C/T). So more correct answers and less average response time, leads to higher score.
The problem is that I prefer to reduce impact of T on scores (C is more important) but I don't know What is the best formula.
One method is to normalise your two parameters so they give answers between 0 and 1 and then apply a weighting to each when combining them. Thus $C_N$ and $T_N$ are the normalised response time and with $C_{max}$ the maximum possible score and $T_{min}$ the minimum possible response time.
Therefore $C_N=C/C_{max}$ and $T_N=T_{min}/T$
You can now attach the weighting e.g. $0.75*C_N+0.25*T_N$ . If you use percentage weightings that add up to 1 (100%) then the output from the formula will always be a number between 0 and 1 which can then be scaled and rounded appropriately.