Basic format of any hypothesis test

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The general procedure for any null hypothesis test is very simple, and contains three stages:

• Step 1: Formulate the null hypothesis
• Step 2: Estimate the p value
• Step 3: Draw your conclusions

Step 1: Formulate the null hypothesis

This is an imaginary world, in which the thing, which really interests you, does not happen. In hypothesis test 1, the null hypothesis is that volunteer Y is not telepathic and can only guess. In test 2, the null hypothesis is that there is no difference, on average, between the marks of male and female candidates in the exam.

Step 2: Estimate the p value

This stands for 'probability' - of results like those actually observed, or more extreme than those observed, if the null hypothesis is true. It tells you how likely the results are to have occurred, if the null hypothesis is true. (An alternative term for a p value is significance level.)

Step 3: Draw your conclusions

The lower the p value, the less plausible the null hypothesis is, and so the more plausible it is that something unusual is occurring. In test 1, the p value for the one card experiment was 2%, and for the two-card experiment it was 0.04%. The second experiment provides far stronger evidence for telepathy than the first: this is indicated by the lower p value for the second experiment. There is a similar distinction between the two p values in the second example.

The important thing to remember is the null hypothesis. Whenever you see a p value, there must be a null hypothesis on which it is based. The null hypothesis represents a baseline assumption against which reality is tested. It is important to imagine this null hypothesis, and to see how it works. Then you will be in a position to see how the p value is estimated, because it is always estimated on the assumption that the null hypothesis is true.

This content has been written by Michael Wood author of Making Sense of Statistics