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# Worked example identifying observational study

AP.STATS:
DAT‑2 (EU)
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DAT‑2.A (LO)
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DAT‑2.A.3 (EK)
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DAT‑2.B (LO)
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DAT‑2.B.3 (EK)

## Video transcript

- [Instructor] So we have a type of statistical study described here. I encourage you to pause this video, read it, and see if you can figure out, is this a sample study, is it an observational study, is it an experiment? And then also think about what type of conclusions can you make based on the information in this study. Alright, now let's work on this together. British researchers were interested in the relationship between farmers' approach to their cows and cows' milk yield. They prepared a survey questionnaire regarding the farmers' perception of the cows' mental capacity, the treatment they give to the cows, and the cows' yield. The survey was filled by all the farms in Great Britain. After analyzing their results, they found that on farms where cows were called by name, milk yield was 258 liters higher on average than on farms where this was not the case. Alright, so they're making a connection between two variables. One was whether cows called by name, whether, whether cows named, alright. Whether cows named and this would be a categorical variable because for any given farmer it's gonna be a yes or a no, that the cows are named, and so they're trying to form a connection between whether the cows are named, and, and milk yield. And this would be a quantitative variable, 'cause you can, you're measuring it in terms of number of liters. Milk, milk, yield. Whether we are drawing a connection. And they are able to draw some form a connection. They're saying, hey when the cows were called by name, milk yield was 258 liters higher on average than on farms where this was not the case. So first is the thing of what type of statistical study this is, and we could think, okay, is this a sample study, is this a sample study, is this an observational study, observational, or is this an experiment? Now, a sample study, experiment, a sample study, you would be trying to estimate a parameter for a broader population. Here, it's not so much that they're estimating the parameter, they're trying to see the connection between two variables, and that brings us to observational study, 'cause that's what an observational study is all about. Can we draw a connection, can we draw a positive or a negative correlation between variables based on observations? So we surveyed a population here, the farmers in Great Britain, and we are able to draw some type of connection between these variables. And so this is clearly an observational, an observational study. Now this is not an experiment. If it was an experiment, we would take the farmers and we would randomly assign them into one or two groups. And in one group we would say, don't name, no name, no naming, and in the other group we would say, name your cows. And then we would wait some period of time and we would see the average milk production going into the experiment in the no naming group and the naming group, and then we would see, we wait some period of time, six months, a year, and then we would see the average milk production after either not naming or naming the cows for six months. So this is not what occurred here. Here we just did the survey to everybody and we just asked them this question, and we were able to find this, we were able to find this connection between whether the cows were named and the actual milk yield. So clearly, not an experiment, this was an observational, observational study. Now the next thing is, what can we conclude here? We know when, you know, they're telling us that when the cows were named, it looks like there was a 258 liter higher yield on average. So, the conclusion that we can strictly make here, is like, well, for for farmers in Great Britain there's a correlation, a positive correlation between whether cows are named and the milk yield. So that we can say for sure. So let me write that down. So for Great Britain, for, for Great Britain farmers, Great Britain farmers, farmers, we have a positive correlation. Positive correlation between naming cows, between naming cows and milk yield. And milk yield. That's pretty much what we can say here. Now, some people might be tempted to try to draw causality. We'll see this all the time where you see these observational studies, and people try to hint that maybe there's a causal relationship here, maybe the naming is actually what makes the milk yield go up. Or maybe it's the other way, the cows produce a lot of milk, the farmers like them more and they wanna name them, because it's like hey, that's my high milk producing cow. So, there's a lot of, there's a lot of temptation to say, you know naming, that maybe there's a causality that naming causes more milk, more milk, or that maybe more milk causes naming. You know, the farmers really like that cow, so they start naming them, or whatever, whatever it might be. But you can't make this causal relationship based on this observational study. You might've been able to do it with a well constructed experiment, but not with an observational study. And that's because there could be some confounding variable that is driving both of them. So, for example, that confounding variable might just be a nice farmer. A nice farmer. And you know we can define nice in a lot of ways, they're gentle, they, and a nice farmer is more likely to name, and a nice farmer's more likely to get, gets a higher yield. And the reason why this is a confounding variable, if you were to control for that, if you just take, well let's just control for nice farmers and then see if naming makes a difference. It might not make a difference. If the farmer is, you know, petting the cows and treating them humanely, and doing other things, it might not matter whether the, whether the farmer names them or not. Likewise, if you take some less nice farmers who, you know, hit their cows, and and they have really inhumane conditions, it might not make a difference whether they name the cows or not. And so it's very important that you, from the observational studies, you might, if they're well constructed, you might be able to make a, you might be able to say there's a correlation, but, you won't be able to make a, drive a causal, or make a causal conclusion.
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