Sunday, 14 June 2015

I can read your mind - now that is what I call an hypothesis test.

A few days ago we were talking on one of the twitter chats about hypothesis testing and I alluded to a fun introduction to the topic I had used before, which I thought I would take the time to flesh out in more detail.

It starts by explaining to pupils that you are going to test if any of them are psychic. Obviously it is nice to ham this up a little bit, give it a bit of dramatic flair etc. Explain to them that the test is that you are going to flip a coin 20 times and keep each result hidden from them. You are then going to concentrate very hard on the result and they have to write down the impression they get from you.

Do the experiment and then see how the kids get on; normally about the maximum you will get is 13 or 14 (any more and you may well actually have a psychic on your hands!) and so the conversation turns to, "well is this enough evidence? What is the probability of someone getting 13/14 by random guessing? How many would be good enough?" This gives me all the tools I need to form a formal hypothesis and discuss things like the significance level (at what point does the probability become so remote we have to agree this is not happening by chance - when it is less than 5%? 1% etc), confidence interval (how many must someone get right before we believe they can read minds) etc.

I find that having this early practical hook to keep coming back to really helps pupils as they navigate what can be quite a tricky topic simply because of the sheer number of different contexts to which it can be applied. So the next time you are teaching kids about hypothesis testing, try giving them a fun hypothesis they can see practically happening in front of them.

P.S. to develop it, ask about what would happen if you switched the coin for a die, and how that would change their views on how many needed to be sure etc...

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