Symmetric hypotheses

In some situations there is a kind of symmetry between the two competing hypotheses. The sample data provide information about which of the two hypotheses is true.

Election poll

A poll is conducted to find which of two candidates is likely to win an election.

Null and alternative hypotheses

In statistical hypothesis testing, the two hypotheses are not treated symmetrically in this way. We must distinguish in a much more fundamental way between them.

Regardless of the data, the strongest we can say supporting H0 is that the data are consistent with it.

We can never conclude that H0 is likely to be true.


Market share estimation through audits

In this example, the null and alternative hypotheses are different in character.

The distinction between the null and alternative hypotheses is so important that we repeat it below.

We never try to 'prove' that H0 holds, though we may be able to 'prove' that HA holds.