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 ${\hat{p}}_F=2383/6640=0.359$;
• The proportion of males who skipped breakfast is ${\hat{p}}_M=1944/6846=0.284$.

Also,

• $\text{Odds}\left(\text{Skips breakfast, among F}\right)=2383/4257=0.5598$;
• $\text{Odds}\left(\text{Skips breakfast, among M}\right)=1944/4902=0.3966$.

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

$$\begin{array}{cc}\text{OR}& =\frac{\text{Odds}\left(\text{Skipping breakfast, for females}\right)}{\text{Odds}\left(\text{Skipping breakfast, for males}\right)}\\ & =\frac{0.5598}{0.3966}=1.41;\end{array}$$ 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