Full Answer Section

• Nonspuriousness: This means that the relationship between the independent and dependent variables cannot be explained by another variable. In the experiment you described, it is possible that another variable, such as the participants’ expectations or the severity of their headaches, could explain the difference in results between the two groups. However, the researchers could try to control for these variables by using a more rigorous design, such as a double-blind placebo-controlled trial.

Based on the information you provided, it is difficult to say definitively whether causality was established in the experiment you described. The experiment did meet the first two conditions (empirical association and appropriate time order), but it is possible that there were other variables that could explain the results.

Here are some additional considerations:

• The sample size was small, so the results may not be generalizable to the larger population.
• The experiment was only conducted once, so it is possible that the results were due to chance.
• The researchers did not control for all potential confounding variables, such as the participants’ expectations or the severity of their headaches.

To improve the experiment and increase the confidence that causality was established, the researchers could:

• Increase the sample size.
• Conduct the experiment multiple times.
• Control for all potential confounding variables.
• Use a double-blind placebo-controlled trial design.

Overall, the experiment you described provides some evidence to suggest that pain relievers can be effective in reducing the frequency of headaches. However, more research is needed to confirm this finding and to rule out other possible explanations for the results.