Testing hypotheses is a common part of statistical inference. To formulate a test, the question of interest is simplified into two competing hypotheses, between which we have a choice. The first is the null hypothesis, denoted by H0, against the alternative hypothesis, denoted by H1 .
For example with 50 years of annual rainfall totals a hypothesis test could be whether the mean is different in El Nino and Ordinary years. Then usually
• The null hypothesis, H0, is that the two means are equal, i.e. there is no difference.
• The alternative hypothesis, H1, is that the two means are unequal, i.e. there is a difference.
If the 50 years were considered as being of three types, El Nino, Ordinary, La Nina then usually:
• The null hypothesis, H0, is that all three means are equal.
• The alternative hypothesis, H1, is that there is a difference somewhere between the means.
The hypotheses are often statements about population parameters. In the first example above it might be:
• H0, is that µE = µO.
• H1, is that µE ≠ µO.
The outcome of a hypothesis test is either
• Reject H0 in favour of H1, or
• Do not reject H0.