Personality & Individual Differences · Simplified
Equally Accurate, or Equally Fast
One dial, two outcomes, and a single measurement that cannot tell you which of them you are looking at.
Before you start
Nothing here is timed and nothing measures you. The two people are fictional and their behaviour is produced by a formula. Nothing on this page assesses the reader, and nothing it shows is about intelligence, impulsivity, attention or anything clinical.
Step 1 of 2
First, a prediction
Two people do the same simple discrimination task, deciding over and over whether a row of arrows points mostly left or mostly right. They turn out to be equally accurate, and one of them is consistently faster. What can you conclude about the faster one?
Step 2 of 2
The two of them, and one dial
Here are the two people from the prediction. Neither of them changes from here on. The only thing you control is how much evidence the second one waits for before answering.
Key terms
- Response caution
- How much evidence somebody waits for before committing to an answer. Raising it raises accuracy and raises time together, which is why one outcome measure cannot be read on its own.
- Speed and accuracy together
- Plotted on the same axes, a person's possible performances form a curve. Where they sit on their curve is a strategy. Which curve they are on is the thing a test is usually trying to find out.
- Discrimination on this task
- How clearly this particular task's evidence arrives for this particular person. It is a property of a person meeting a task, not a general ability, and it is not intelligence.
Each line is everything one person could produce on this task, as their caution runs from low to high. The marked points are where the two of them are now. A line lying above and to the left of another means better performance at every speed.
What this shows
The curve is the person. A point on it is a decision.
Key idea: The two lines never cross. At every speed the first person is more accurate, and at every accuracy they are faster, so on this task they are better at it in the only sense that does not depend on strategy. And yet by moving one dial, which changes nothing about either of them, you can make the pair look identical on accuracy or identical on time. That is what makes a single outcome measure uninterpretable: an accuracy score does not say whether somebody found the task hard or was being careful, and a time does not say whether they found it easy or were being hasty. Only both together locate a person on their curve, and only knowing where they are on it tells you which curve they are on. The practical version is that a test reporting one number, whether that number is a score or a time, has already thrown away what it would take to interpret it.
Two fictional people whose behaviour is produced by a formula, chosen so that one clearly outperforms the other; real pairs are frequently not orderable at all, with curves that cross so that who looks better genuinely depends on the speed you compare them at. Three cautions. What differs between these two is how clearly this task's evidence arrives for each of them, which is a property of a person meeting a particular task rather than a general ability, and it is not intelligence. Caution is treated here as a dial somebody sets, whereas in practice it responds to instructions, to fatigue, to what is at stake, and to what a person has understood the task to be asking for. And the model has no error in it at all: real data give an estimate of where somebody sits with uncertainty around it, not a point.
The longer version includes the discrimination task itself, which you perform, along with practice trials, three contrasting fictional strategies and a difficulty control. It is at Speed-Accuracy Trade-Off in the main collection.