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## AP®︎/College Statistics

### Course: AP®︎/College Statistics > Unit 6

Lesson 1: Introduction to planning a study- Identifying a sample and population
- Identify the population and sample
- Generalizability of survey results example
- Generalizability of results
- Types of studies
- Worked example identifying observational study
- Invalid conclusions from studies example
- Types of studies

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# Worked example identifying observational study

AP.STATS:

DAT‑2 (EU)

, DAT‑2.A (LO)

, DAT‑2.A.3 (EK)

, DAT‑2.B (LO)

, DAT‑2.B.3 (EK)

CCSS.Math: Worked example identifying observational study.

## Want to join the conversation?

- How could you have a Sample study and it not be an Observational or Experimental study as well? You sample the population, but how do you get data from it without using Observation or Experimentation?

Shouldn't it be Observation and Experimentation, and Sample or Non-Sample be methods of performing those study methods?

I.E. Sample Observation, Sample Experimentation, non-Sample (or population?) Observation, or something like that?(6 votes)- A sample study is a way to estimate the value of some data over all the member of the population by just sampling randomly over some percentage of the population. i.e. We want to know how many percentage of US citizens play chess, and we estimate the number by sampling (asking) randomly over 5000 citizens to estimate the real percentage.

Experimental study is basically a comparison experiment between two groups, the test (treatment) group and the control group to reveal whether there's a causality relation between the treatment and the effect observed.

The objective of observational study is to find a correlation between two variables by observing over a sample, i.e. survey over some random people to know the relationship between sugar intake and heart disease risk.(15 votes)

- Why would the association be more appropriate in this case?(4 votes)
- Association refers to a more general analysis of two variables whereas correlation refers to a specific measure (The Pearson Correlation Coefficient) between two variables of a
**linear**relationship in particular.(1 vote)

- The details of the problem here seem vague. We actually can't really say if the 258 liters are significant or not. Was that 258 liters per cow? per farm? for the entire population of named cows? And was this per day, per month or per year? If the change in milk production was an increase over some 5000 liters of milk, then, yes, of course it suggests a correlation. But if it was an increase above a couple of million liters of milk, that's only about .01% increase. Then the number is not at all statistically significant, and doesn't suggest any correlation at all.

Am I missing something?(3 votes) - Why's association more appropriate ?4:19(2 votes)
- A question stated:

The mayor of Statville has to decide how to allocate her education budget between the two high schools in town, “Stat Sticks” and “Datum High.” To decide which school deserves a bigger portion of the budget, she went over the grade sheets of the students from both schools in the past 5 years, and analyzed the data. She found that the overall grade average of “Stat Sticks” students is 4 points higher than the overall grade average of the students of “Datum High.”

And the answer to "what valid conclusion can be made from the result?" was

Students from “Stat Sticks,” in the last 5 years, had higher grades, on average, than students from “Datum High.”

But there was another option that specified the overall grade for each student being 4 points higher, I was wondering why that one was incorrect and the one more generally saying it was higher was correct.(1 vote) - The observational study shows a positive correlation between farmer perception of cow's mental capacity and milk yield, and there are two clusters explained by "naming" and "no naming" where the naming cluster has a higher milk yield on average. Am I right ?(1 vote)
- Researchers only observe the subjects and do not interfere or try to influence the outcomes.(1 vote)

## 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.