Testing hypotheses

In chapter 5 we established how to determine the confidence intervals for a single result obtained from a sample. The next issue to be considered covers the situation where we wish to investigate a specific hypothesis relating to a result obtained from one or more samples.

With confidence intervals the implicit hypothesis is that the specified interval contains the required value. With hypothesis testing the hypothesis is made explicit, and can be framed so as to refer to particular values of the population statistic. It might, for example, be a hypothesis relating to a comparison of the results of two different samples. Or it might be a hypothesis about whether or not the result of a single sample can be considered as different from some specified value.

For example, RELIEF in the sample of Kent parishes has a mean value of 20.28 shillings with a standard deviation of 7.64 shillings. For Sussex the corresponding values are a mean of 26.04 shillings and a standard deviation of 8.04 shillings. The mean in Sussex was thus almost 6 shillings (28 per cent) higher than the mean in Kent.

This differential might have occurred, either

1. (a) because of chance factors and accidental irregularities reflected in the samples we happened to get from the two counties; or

2. (b) because there were systematic and consistent differences in the underlying structural features of the two counties; for example, in the sources of income available to labourers, the generosity of relief payments, or the incidence of poverty and sickness in the two areas.