## Hypotheses

The first step in tests of significance is to make a claim which one then has to find evidence against. This statement is called the null hypothesis. The test is intended to determine the strength of the evidence against the null hypothesis. Customarily, the null hypothesis is a statement of no difference or no effect. The term null hypothesis is abbreviated as H0 and is usually stated in terms of some population parameter or parameters. For example, suppose that p1 is the proportion of the whole population of British males who would have been illness free in 1999 had they ridden a bicycle to work each day and let p2 stand for the illness-free proportion had they gone to work in their cars instead. The null hypothesis is:

because this states that riding a bicycle to work has the same effectiveness as travelling by car. The name given to the statement we hope or suspect is true instead of H0 is called the alternative hypothesis, abbreviated by H1. The alternative hypothesis in this case is that riding a bicycle to work is more effective than travelling by car. In terms of the population parameters this is:

A test of significance assesses the strength of the evidence against the null hypothesis in terms of probability. If the observed outcome is unlikely under the supposition that the null hypothesis is true, but is more probable if the alternative hypothesis is true, that outcome is evidence against H0 in favour of H1. The less probable the outcome is, the stronger is the evidence that H0 is false.

There are many tests of significance appropriate for different types of hypothesis and for different data-collection designs - as well as levels of significance. Some of these are examined later. An outline of what such a test of significance should include is shown in the box.

### STEPS IN A TEST OF SIGNIFICANCE

1 Select the null hypothesis H0 and the alternative hypothesis H1. The test is designed to assess the strength of the evidence against the null hypothesis. H1 is a statement of the alternative we will accept if the evidence enables us to reject H0.

2 Select the level of significance. This states how much evidence against H0 we will accept as sufficient.

3 Select the test statistic on which the test will be based. This is a statistic that assesses how well the data conform to H0.

4 Find the probability value that the test statistic would weigh against H0 at least as strongly as it does for these data, were H0, in fact, true. If the probability value is less than or equal to the significance level then the test was statistically significant at that level.

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