Type 1 and 2 errors are not easy to understand and recently one student (thank you Laura Hastings) wrote in to ask if we were also confused (!) and had made a mistake with Type 1 and 2 errors in our AQA A A2 book. Fortunately we hadn’t but the explanation was a bit unclear. On page 266 (Chapter on Anomalistic Psychology) it says:

Causal thinking evolved because it allows people to understand and control their environment, i.e. to be able to predict that, for example, if you eat a red mushroom you will die. This causal thinking is adaptive but may sometimes lead to Type 1 errors – where you believe something is true when it isn’t, for example you believe that tying your shoes laces twice causes luck.

The problematic phrase is ‘where you believe something is true when it isn’t’. Laura was confused because a Type 1 error is defined on page 300 as ‘when a null hypothesis is rejected when it is true’. So it sounds like we got it wrong – but in fact both Type 1 and Type 2 errors are ‘where you believe something that isn’t true’:

• Type 1 error (false positive) – you believe the null hypothesis isn’t true (and reject it) but in reality the null hypothesis is true. So, in the case of shoe laces you believe shoe laces and luck are linked but, in reality, there is no link. Or you avoid mushrooms for ever after because you think they will make you die but this link is mistaken.
• Type 2 error (false negative) – you believe the null hypothesis is true (and accept it) when in reality the null hypothesis is not true. In the case of shoe laces and luck, you believe tying your shoe laces twice has no effect on luck but in fact it has. Or you believe that red mushrooms don’t cause death but they do.

The point is that we err on the side of making Type 1 errors (and believing erroneous causal relationships) because we might otherwise make Type 2 errors.

As for the text book, it would be better if it said ‘Type 1 errors – where you believe the null hypothesis is wrong when it isn’t’.