# Reaction timer timer

How can you time the reaction timer?

The reaction timer problem introduces this interactivity which measures the amount of time taken to react to a shape appearing on-screen:

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In this interactivity it is known that once a shape disappears an internal timer begins. The time until the appearance of the next shape is determined randomly through a clear, well-defined statistical process which is unknown to us. From the moment that this next shape disappears the timer resets and starts again; the random process then again determines the time until the appearence of the next shape. Familiarise yourself with the interactivity before considering this question:

- Upon each shape disappearing there is a delay of a random length until the appearence of the next shape. How might you design an experiment to determine the nature of the random process giving rise to the delay?

You might need a stopwatch. How might you estimate your reactions in stopping the stopwatch?

Also, there is a very clear and precise explanation for the lengths of time that elapse before the stars appear.

The timer gives us our reaction time, but tells us nothing about the random process it implements. One way to find how long the shape disappears for would be to use a stopwatch and click after a known interval. Provided this interval is big enough, subtracting the reaction time will give us the time from the shape's disappearence to its reappearance.

Carry this out a number of times and plot your data. What does the distribution look like? Does your experimental evidence support a conjecture for how the random process works?

Alexander from Wesley College thinks that he observed a difference between the reflexes for left and right hands. We wonder if this could be used to test people who claim to be ambidextrous?

I think that beause I'm right handed, when the star appeared or the moon I found I had an instant reflex. But when I used my left hand I had to think about it because I'm right handed. All up its about reflex.

### Why do this problem ?

This problem gives students a real statistical challenge to address. It can be accessed at various levels and includes issues of measurement, sampling and hypothesis testing. At the highest level, students can create a hypothesis for a distribution and then test that hypothesis.### Possible approach

The issues of experimental design could be discussed as a
class. The interactivity purposely does not provide the time
between stars disappearing and reappearing. Students will need to
realise this and then suggest ways of gathering these data. There
will be questions of measuring the data and it is hoped that
students will realise that
collecting the data will involve a reaction delay and might relate
this to the original purpose of measuring the reaction time.
Students should be encouraged to design the experiment as
rigorously as they are able to, given the practical constraints of
having to run the interactivity to collect the data. (Note: they
will probably need their own stopwatch)

How can the data be analysed once collected? Students can
apply statistical concepts as appropriate to their level of study.
The data can be represented in ways appropriate to their level of
study. They might then begin to suggest possible distributions to
fit the data.

It is hoped that, given enough data, students will notice that
there are no very short times and no very long times. Would this be
compatible with normal or Poisson distributions?

### Key questions

How are we to collect the times for the stars to appear?

Is there a reaction delay in collecting this time?

How might we design the experiment to minimise the effects of
reaction time uncertainty?

What distributions or statistical measures do we know?

Once we have our data how might we rule out certain
distributions?

How much data would we need to be confident in a final
hypothesis?

### Possible extension

This task naturally offers differentiation by outcome. Students might want to try to write up clearly the process for display; collecting mathematical thoughts in this way is a useful exercise.### Possible support

Suggest measuring data and plotting a histogram of times with
an interval of 0.5 seconds to begin to get a feel for the
data.

Alternatively, you can use the reaction timer to pose and test
your own hypotheses about reaction. You might like to see the
problem Reaction
Timer to get some ideas.