14.5 Example: Skipping breakfast

The data in Table 14.6 come from a study of Iranian children aged 6–18 years old (Kelishadi et al. 2017). From this table:

  • The proportion of females who skipped breakfast is \(\hat{p}_F = 2\,383/6\,640 = 0.359\);
  • The proportion of males who skipped breakfast is \(\hat{p}_M = 1\,944/6\,846 = 0.284\).

Also,

  • \(\text{Odds}(\text{Skips breakfast, among F}) = 2\,383/4\,257 = 0.5598\);
  • \(\text{Odds}(\text{Skips breakfast, among M}) = 1\,944/4\,902 = 0.3966\).

For example, about 55.98 females skip breakfast for every 100 females who eat breakfast. The odds ratio (OR) comparing the odds of skipping breakfast, comparing females to males, is

\[\begin{align*} \text{OR} &= \frac{\text{Odds}(\text{Skipping breakfast, for females})}{\text{Odds}(\text{Skipping breakfast, for males})}\\ &= \frac{0.5598}{0.3966} = 1.41; \end{align*}\] the odds of females skipping breakfast are \(1.41\) times the odds of males skipping breakfast. The data can then be summarised numerically (Table 14.7).

TABLE 14.6: The number of Iranian children aged 6 to 18 who skip and do not skip breakfast
Skips breakfast Doesn’t skip breakfast Total
Females 2383 4257 6640
Males 1944 4902 6846
TABLE 14.7: Numerical summary of the Iranian-breakfast data: Odds and percentage of those who skip breakfast
Percentage Odds Sample size
Females 64.1 1.786 6640
Males 71.6 2.522 6846
Odds ratio 0.708