Types of studies | AP Statistics | Khan Academy

In this video, we're going to get our bearings on the different types of studies you might statistically analyze or statistical studies.

So, first of all, it's worth differentiating between an experiment and an observational study. I encourage you to pause this video and think about what the difference is, at least in your head, between an experiment and an observational study.

Well, you might already be familiar with experiments. You oftentimes have a hypothesis that if you do something to one group, that it might have some type of statistically significant impact on them relative to a group that you did not do it to, and you would be generally right. That is the flavor of what we're talking about when we're talking about an experiment.

An experiment involves actively putting people or things into a control versus treatment group. In the treatment group, you put the people, and you usually would want to randomly select people into the treatment group. Maybe it's a new type of medication, and in the treatment group, they actually get the medication, while in the control group—which you would put people into randomly, whether they're in control or treatment—here they might get a placebo, where they get a pill that looks just like the medication but it really doesn't do anything.

Then you wait some time, and you can see is there a statistically significant difference between the treatment group on average and the control group. So that's what an experiment does. It's kind of this active sorting and figuring out whether some type of stimulus is able to show a difference.

While an observational study, you don't actively put people into groups. Instead, you just collect data and see if you can have some insights from that data. If you can say, "Okay, the data shows there’s a population here; can I come up with some statistics that are indicative of the population?" I might just want to look at averages, or I might want to find some correlations between variables.

But even when we're talking about an observational study, there are different types of it, depending on what type of data we're looking at—whether the data is backward-looking, forward-looking, or it's data that we are collecting right now based on what people think or say right now.

So if we're thinking about an observational study that is looking at past data, I could imagine doing something like this at Khan Academy. We could look at maybe usage of Khan Academy over time. We have these things in our server logs, and we're able to do some analysis there.

Maybe we're able to analyze and say, "Okay, on average, students are spending two hours per month on Khan Academy over in 2019." That would be past data, and that type of observational study would be called a retrospective study. Retro means backward, and spective means looking. So, a retrospective observational study would sample past data in order to come up with some insights.

Now you can imagine there might be the other side. What if we are trying to observe things into the future? Well, here you might take a sample of folks who you think are indicative of a population, and you might want to just track their data.

So, you could even consider that to be future data. You pick the group, the sample ahead of time, and then you track their data over time. I'm just going to draw it as these little arrows that you're tracking their data, and then you see what happens.

For example, you might randomly select, hopefully, a random sample of 100 women, and you want to see in the coming year how many eggs do they eat on average per day. Well, what you would do is you selected those folks, and then you would track that data for each of them every day.

Once you have the data, you could actually do it while you're collecting it, but at the end of the study, you'll be able to see what those averages are. You can also keep track of it while you're taking that data. You could imagine, instead of retrospective, we're now looking forward. So it is a prospective, forward-looking observational study.

Last but not least, some of you all are probably thinking, "What about if we're doing something now?" If we go out there and we were to survey a bunch of people and say, "How many eggs did you eat today?" or "Who are you going to vote for?" What might we call that?

It was tempting to call it something with a prefix and "inspective," so it all matches. But it turns out that the terminology the statisticians will typically use is a sample survey. A sample survey is where, right now, you're going to take a hopefully random sample of individuals from the population that you care about, and you are just going to survey them right now and ask them, say, some questions or observe some data about them right now.

So, I'll leave you there. This video is to just give you a little bit of the vocabulary and a little bit of a taxonomy on the types of studies that you'll see in general, which is especially useful to know when you're exploring the world of statistics.