ABSTRACT
Here one can notice that the sample size is eighty cases, an apparently reasonably sized sample. However, six of the ten cells of responses (60 per cent) contain fewer than five cases. The chi-square statistic requires there to be five cases or more in 80 per cent of the cells (i.e. eight out of the ten cells). In this example only 40 per cent of the cells contained more than five cases, so even with a comparatively large sample, the statistical requirements for reliable data with a straightforward statistic such as chisquare have not been met. The message is clear, one needs to anticipate, as far as one is able, some possible distributions of the data and see if these will prevent appropriate statistical analysis; if the distributions look unlikely to enable reliable statistics to be calculated then one should increase the sample size, or exercise great caution in interpreting the data because of problems of reliability, or not use particular statistics, or, indeed, consider abandoning the exercise if the increase in sample size cannot be achieved.
