A crossover study on comparing a magnetic device to placebo for reducing pain in 54 people suffering from low back or knee pain (neuromagnetics.mc.vanderbilt.edu/publications) reported a significant result overall, the magnetic device being preferred to placebo. However, when the analysis was done separately for the 27 people with shorter illness duration and the 27 people with longer illness duration, results were not significant. Explain how it might be possible that an analysis could give a P-value below 0.05 using an entire sample but not with subgroups, even if the subgroups have the same effects. (Hint: What is the impact of the smaller sample size for the subgroups?)