times is statistically significant, and you can be 95 per cent confident that this difference is between 4 and 39 minutes.

Exercise 10.3 Table 10.4 includes the sample median times and their 95 per cent confidence intervals for each time interval, for both groups separately. Only one pair of confidence intervals don’t overlap, those for the only time difference which is statistically significant. Why aren’t you surprised by this?

Estimating the difference between two matched population medians – Wilcoxon signed-ranks method

When two groups are matched, but either the data is ordinal, or if metric is noticeably skewed, you can obtain confidence intervals for differences in population medians, based on the nonparametric Wilcoxon test. The two population distributions, regardless of shape, should be symmetric. This is the non-parametric equivalent of the parametric matched-pairs t test, described above. The matching will again reduce the variation within groups, so narrower, and therefore more precise, confidence intervals are available for a given sample size.

Briefly the Wilcoxon method starts by calculating the difference between each pair of values, and these differences are then ranked (ignoring any minus signs). Any negative signs are then restored to the rank values, and the negative and positive ranks are separately summed. If the medians in the two groups are the same, then these two rank sums should be similar. If different, the Wilcoxon method provides a way of determining whether this is due to chance, or represents a statistically significant difference in the population medians.

An example from practice

Table 10.5 contains the results of a case-control study into the dietary intake of schizophrenic patients living in the community in Scotland (McCreadie et al. (1998). It shows the daily energy intake of eight dietary substances for the cases (17 men and 13 women diagnosed with schizophrenia), and the controls, each individually matched on sex, age, smoking status and employment status.

If you focus on the penultimate column, in which data for men and women is combined, you can see that only the confidence interval for daily protein intake, (−1.1 to 32.8) g, contains zero, which implies that there is no difference in population median protein intake between schizophrenics and normal individuals. For all other substances, the difference is statistically significant.

Exercise 10.4 Explain the meaning of the 95 per cent confidence interval for difference in median alcohol intake of the two groups in Table 10.5.