Introduction

Every time you make a decision based on the probability of a particular result, there is a risk that your decision is wrong. There are two sorts of mistakes you can make and these are called Type 1 error and Type 2 error.

Type 1 error

A Type 1 error or false positive occurs when you decide the null hypothesis is false when in reality it is not. Imagine you have taken a sample of size n from a population with known statistics of μ and σ and subjected this sample to a particular experimental treatment. Because the population statistics are known you could test whether this sample mean was significantly different to the population mean by doing a Z test (Section 8.3).

If the treatment had no effect the null hypothesis would apply and your sample would simply be equivalent to one drawn at random from the population. Nevertheless, 5% of the sample means of size n will lie outside the 95% confidence interval of μ ± 1.96 SEM. Therefore, 5% of the time you would incorrectly reject the null hypothesis of no difference between your sample mean and the population mean (Figure 9.1) and accept the alternate hypothesis. This is a Type 1 error.

It is important to realize that Type 1 error can only occur when the null hypothesis applies. There is absolutely no risk if the null hypothesis is false.