Invalid conclusions from studies example | Study design | AP Statistics | Khan Academy

Jerry was reading about a study that looked at the connection between smartphone usage and happiness. Based on data from approximately 5,000 randomly selected teenagers, the study found that, on average, the teens who spent more time on smartphones were significantly less happy than those who spent less time on smartphones. Jerry concluded that spending more time on smartphones makes teens less happy.

Alright, this is interesting! So what I want you to do is think about whether Jerry is making a valid conclusion or not, and why or why not. Do you think he's making a valid conclusion?

Alright, now let's work on this together. This is really important to understand because you will see things like this in the popular media all the time. They try to establish a causality when there might not be causality, or at least where the study might not be able to show causality.

So right now, Jerry is saying he's concluding that smartphone usage makes teens less happy. He's assuming there's a causal connection: smartphone usage causes teens to be less happy. Can he actually make that conclusion from this study, based on how it was designed?

Well, the first thing to ask ourselves is, is this an experimental study that is designed to establish causality, or is it an observational study where we really can just say there's an association? But we really can't make a statement about causality.

In an experimental study, he would have had to have a control group and then a treatment group, sometimes called an experimental group. So I'll say that's the control group, and that's the treatment or the experimental group. Then, you randomly assign folks to one of those two groups. You would make that treatment group use the cell phone more and see if they are less happy.

That's not what happened here. What happened here was an observational study. In this study, we are looking at two variables: smartphone usage and then teen happiness. They took these 5,000 randomly selected teenagers and they figured out their smartphone usage and their happiness, maybe with a survey of some kind.

Then you could plot those data points. You would have 5,000 data points. This data point right over here would be a very happy teenager that doesn't use a smartphone much. This would be a not-so-happy teenager that uses a smartphone a lot. You would plot those data points, and there might be a teenager who's unhappy and doesn't use a smartphone, or one that is happy and that uses a smartphone a lot.

But you could see there's a trend, there's an association that, in general, the teenagers who use their smartphones more seem to be less happy, and the teenagers who use their smartphones less seem to be more happy.

But it's important to realize that the causality could go the other way around. Maybe less happy teenagers use their smartphones more, and maybe more happy teenagers don't find a need to use a smartphone. Or there could be some variable that's not even being observed in the study that has a causal relationship with both of these.

So there could be some other variable that might cause someone to be less happy and use their smartphone more. In an observational study, you can really just say there's an association; you wouldn't be able to say that there is causality.

So, Jerry is not making a valid conclusion. It's an observational study. We've only established an association, not causality.