# Teaching the Runs Test for Randomness

The other day in my statistics class, I was teaching the runs test for randomness.  One of my students keeps on asking for an in-class activity, and it happened that I had an extra half-an-hour of class time to spare.  So, I adapted this famous teaching experiment for use in my own class.

The set-up:  I split the class into 8 groups, with 3-4 students in each group.  Four of the groups were labeled ‘Group A’ and the other four groups were ‘Group B’.  Group A went into the hallway while I explained the assignment to Group B.

Group B was the coin tossing group.  They were asked to flip a coin 200 times and record the sequence of heads and tails that they observed.  Once I made sure that Group B understood the instructions, they went into the hallway while I explained the assignment to Group A.

Group A was the random listing group.  They were asked to write a sequence of 200 heads and tails that they thought was random without actually flipping a coin.  Once I made sure that Group A understand the instructions, both groups rejoined in the classroom and started their experiment.

Now, since neither group knew the instructions that the other group was given, or what we were going to do with the data that was collected, it made for a very interesting experiment in itself.  The students came up with very unique ways of recording the data.  Some groups assigned one recorder and then the other two people in the group alternated flips of the coin.  Other groups had everyone in their group flip the coin 50 times in a row simultaneously and then combined their results at the end.  I was OK with this since it would have been no different if the students would have just followed one another in their coin flips.

Finally, each Group A exchanged papers with a Group B and analyzed the sequence using the runs test for randomness.  What I discovered is that because the students did not know why the data was being collected, they did not organize it very well, so the group that they passed it to had a very hard time figuring out what was going on.  This made for a good side discussion on the importance of organizing data properly while it is being collected.

Soon enough the students came up with a process for analyzing the data, most groups used a yellow highlighter to highlight the heads to make the runs a little easier to count.  Once their runs were counted, they were able to analyze their sequence using the runs test for randomness.  The students worked very well together verifying their calculations for the mean and standard deviation of the number of runs.

As suspected, it did turn out that Group A (the random listing group) ended up NOT generating random sequences and that Group B (the coin tossing group) did end up generating random sequences.  This made for an interesting discussion as well, since of course, Group A insisted that their sequence had to be random given the way that they collected their data.