The segmented bar graph reveals that for the children in this sample the incidence of near-sightedness increases as the level of lighting increases. When we have a random sample with two categorical variables, we can perform a chi-squared test of association. Because the expected counts are large (smallest is 14.25 > 5), we can apply the chi-squared test to these data. The p-value of this chi-squared test is essentially zero, which says that if there were no association between eye condition and lighting in the population, then it’s virtually impossible for chance alone to produce a table in which the conditional distributions would differ by as much as they did in the actual study. Thus, the sample data provide overwhelming evidence that there is indeed an association between eye condition and lighting in the population of children like those in this study. A closer analysis of the table and the chi-squared calculation reveals that there are many fewer children with near-sightedness than would be expected in the “darkness” group and many more children with near-sightedness than would be expected in the “room light” group. But remember the main lesson of this study from Chapter 3 — we cannot draw a cause-and-effect conclusion between lighting and eye condition because this is an observational study. Several confounding variables could explain the observed association. For example, perhaps near-sighted children tend to have near-sighted parents who prefer to leave a light on because of their own vision difficulties, while also passing this genetic predisposition on to their children. We also have to be careful in generalizing from this sample to a larger population because the children were making voluntary visits to an eye doctor and were not selected at random from a larger population.