Question

Pesticides and ADHD Are children with higher exposure to pesticides more likely to develop ADHD (attention-deficit/hyperactivity disorder)? In one study, authors measured levels of urinary dialkyl phosphate (DAP, a common pesticide) concentrations and ascertained ADHD diagnostic status (Yes/No) for 1139 children who were representative of the general US population. \(^{7}\) The subjects were divided into two groups based on high or low pesticide concentrations, and we compare the proportion with ADHD in each group. (a) Define the relevant parameter(s) and state the null and alternative hypotheses. (b) In the sample, children with high pesticide levels were more likely to be diagnosed with ADHD. Can we necessarily conclude that, in the population, children with high pesticide levels are more likely to be diagnosed with ADHD? (Whether or not we can make this generalization is, in fact, the statistical question of interest.) (c) In the study, evidence was found to support the alternative hypothesis. Explain what that means in the context of pesticide exposure and ADHD?

Short answer

The parameters are the proportions of children with or without ADHD among high and low pesticide exposure groups. The null hypothesis states no difference in ADHD occurrence across these groups, while the alternative indicates higher likelihood with greater exposure. Generalizing the conclusion drawn from the sample to the whole population requires statistical support such as hypothesis testing. Evidence favoring the alternative hypothesis indicates a greater likelihood of children with high exposure developing ADHD, although causation isn't confirmed.

Step-by-step solution

Define the parameters, null and alternative hypotheses

The parameters of interest are the proportions of children with ADHD in the groups with high and low pesticide exposure, usually denoted by \(p_1\) and \(p_2\). The null hypothesis could be that the proportion of children who develop ADHD is the same regardless of pesticide exposure level, i.e., \(H_0: p_1 = p_2\). The alternative hypothesis, however, would propose a difference in ADHD occurrence between the groups, specifically stating that children with high pesticide exposure are more likely to develop ADHD. Therefore, the alternative hypothesis could be \(H_a: p_1 > p_2\).

Discussing the possibility of generalization

Although the study found that children with high pesticide levels were more likely to be diagnosed with ADHD in the sample, it's not necessarily appropriate to conclude the same about the overall population. This reservation is due to the possibility of sampling bias or errors in the study, or simply the chance variation in samples. Hence, it would require further statistical testing, such as hypothesis testing to draw such a population-wide conclusion.

Interpretation of the evidence in favor of the alternative hypothesis

If there's evidence to support the alternative hypothesis, it implies that the study's results are statistically significant and not likely due to chance. In this context, it means that children with higher pesticide exposure are more likely to develop ADHD than those with lower exposure. However, note that this does not necessarily prove a causal relationship, as correlation does not always imply causation.