This example from Retraction Watch illustrates how NOT to do research. It is a study that was accepted and retracted from Frontiers in Public Health. It purported to find a link between childhood vaccination and a variety of childhood illnesses. This would be a good case study for Research Methods. In particular, this example illustrates:
1) Retraction of scientific studies
2) The problems with self-report surveys
3) Sampling and trying to generalized from a biased samples
4) What constitutes a small sample size depending on the research you are conducting
5) Conflict of interest
This study, since retracted, studied unvaccinated, partially vaccinated, and fully vaccinated children.
And the study found "Vaccinated children were significantly less likely than the unvaccinated to have been diagnosed with chickenpox and pertussis, but significantly more likely to have been diagnosed with pneumonia, otitis media, allergies and NDDs (defined as Autism Spectrum Disorder, Attention Deficit Hyperactivity Disorder, and/or a learning disability)."
But the study surveyed moms who home school their children. A group that is historically, but not exclusively, anti-vaccination. From the study:
"Homeschool organizations in four states (Florida, Louisiana, Mississippi, and Oregon) were asked to forward an email to their members, requesting mothers to complete an anonymous online questionnaire on the vaccination status and health outcomes of their biological children ages 6 to 12."
And money to conduct this study was crowd sourced via a pro Autism:Vaccination website. There are other problems with this study, as noticed by Retraction Watch as well as the summary piece below. The sample sized used was relatively small for this kind of research, no one verified the various diagnoses via medical records, etc.
So, there is plenty for your students to consider with this study. Maybe you could create a methodology for this study that would fix the current, flawed methodology. Or you could just give your student the summary of the study and ask them to find the problems.
Further treatment (and deconstruction) of the study can be found here.