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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)
CCSS.Math:

## Video transcript

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 that 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 all right 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 when this was not the case all right 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 going to be a yes or 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 because you can you're measuring it in terms of number of liters milk milk yield whether we are drawing a connection and they're able to draw some form of a connection they're saying hey when the cows were called by name milk yield was 258 liters higher on average than on farms when this was not the case so first let's just think about 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 survey tional or is this an experiment now a sample study an experiment a sample study you would be trying to estimate a parameter for a broader population he 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 because that's what an observational study is all about can we draw a connection can we draw a positive or negative correlation between variables based on observations so we surveyed a population here the farmers in in Great Britain and we are able to draw some type of connection between these variables and so this is clearly an observational and observational study now if this this is not an experiment if there 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 will see the average milk production going into the experiment and the no naming group and the naming group and then we will see we wait some period of time six months a year and then we will see the average milk production after either not naming or naming the cows for six months so that's 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 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 litre higher yield on average so the conclusion that we can strictly make here is like well for for for farmers in Great Britain there is 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 you'll see this all the time where you see these observational studies and people try to hint and 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 want to name them it's like hey that's my high milk producing cow so there's a lot of there's there's a lot of temptation to say cow you know naming that maybe there's a cause out of that naming causes more milk more milk or that maybe more milk causes naming your the farmers really like that cow so they they start naming them or or whatever whatever it might be but it's you can't make this causal relationship based on this observational study you might have 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 is more likely to get it 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 let's just control for nice farmers and then see if naming makes a difference it might not make a difference if then if the farmer is you know petting the cows and treating them humanely and doing other things it might not matter whether the 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 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 say there's a correlation but you it's you won't be able to make a drive a causal or make a causal conclusion