WEBVTT

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Normally in a research study, 
we cannot study full populations

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because of practical issues.

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Therefore we have to rely on a sample.

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When we take that sample,

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there are multiple things 
that we need to consider,

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and a number of things that can go wrong,

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that can either produce results that are 
biased or results that are inefficient.

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So let's take a look at some 
issues related to sampling.

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First, we have a population,

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that population is the 
thing that we want to study,

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so we want to say something about the population.

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And let's say we are studying 
that population using a survey,

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that we mailed to companies.

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To send out the invitations to participate,

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we have to have an address for every company.

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So we have to have some kind of 
operational definition of our population.

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So we called operational 
population a sampling frame.

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So the sampling frame is an 
actual list of companies or  

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people or whatever things we're studying.

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And the population is the conceptual 
definition of the thing that we're studying.

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Then from the sampling frame,

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it can be if we are studying 
individuals in Finland for example,

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the sampling frame could come 
from the population register,

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and it could contain millions of people.

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So then from the sampling frame,

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we actually take the sample.

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Typically we choose people randomly,

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so the random sample is the 
simplest way of taking a sample,

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and it is often the most desirable way as well.

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Then we send out our survey and 
some people choose to participate,

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some companies choose to participate,

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others choose to not participate,

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so we get an actual dataset that we can work with.

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Now a number of things can go wrong,

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and we have to take those into consideration.

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So let's take an example of 
what this framework means.

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So let's say we're studying the population 
of young Finnish high technology companies.

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That is a conceptual definition,

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then we need to actually define empirically,

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or have an operational definition of 
what it means to be a young company,

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and what it means to be a technology firm.

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So no one is maintaining a 
list of technology companies,

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so we have to operationalize that concept to a way

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that we can actually get data for.

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So the sampling frame would be, for example,

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business IDs, so registered corporations,

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that is not the same thing as a company,

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so one organization can 
have multiple business IDs.

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But we have to have some kind 
of operational definition

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that we can actually get data for,

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and we can get data from business IDs or 
legal entities behind these companies.

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So let's define young technology companies as

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companies that are zero to three years old,

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and are on certain industry 
codes, for example, 62 or 72,

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those correspond to information 
technology industries.

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So that is our operational definition and that 
allows us to get a list of actual companies.

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Then we get a sample,

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so let's say that

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we get a thousand firms randomly selected 
on a list of maybe ten thousand companies

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or five thousand companies,

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whatever the sampling frame is.

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The reason for taking a sample here,

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that we email is cost,

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so whenever we email or mail,

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the address acquisition, it 
cost some money or some effort,

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and if we mail physical letters, 
then there are printing costs.

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Then we get the actual data,

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for example, ten percent of our informants

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that we're invited to participate 
decide to respond to the survey.

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So what can go wrong with this kind of thing?

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And there are multiple things.

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The relevant question with 
the sampling frame is that,

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does our operational definition of the 
population match the conceptual one?

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So does the frame match the population?

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Then we have, the second question 
is, how large is the sample size?

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Basically, this is randomly chosen then

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the only thing that we can decide is,

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how many observations we get,

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so is thousand enough?

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And when we plan for sample size,

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we have to take the expected 
response rate into consideration.

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So if we expect a ten percent response rate,

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and we need five hundred full 
responses to our analysis.

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Then we should send out the 
invitation to five thousand companies,

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so we would have five thousand randomly 
chosen firms instead of this one thousand.

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Then the most problematic part is that,

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the people who, or companies 
who decide to respond,

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may not be randomly chosen.

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So if we have,

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out of these thousand companies 
that were invited to participate,

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if random 10% respond,

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that only means that we have inefficiency.

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So increasing the sample size would make 
our results or estimates more precise,

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but that's it.

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A more problematic condition occurs if 
this 10 percent are chosen systematically,

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and that leads to bias results.

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For example, if our survey 
was about innovativeness

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and those companies that are more 
innovative or more likely to participate,

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then any regression analysis involving 
innovation as a dependent variable

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would produce biased results.

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Let's take a look at why that happens.

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So this is a classic example 
from Berk's paper 1983,

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and he is demonstrating that there's a 
relationship between education and income

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such that when education increases 
then income goes up as well,

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so it's a linear relationship here.

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So what will happen if people who get 
low-income either don't provide data,

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or these people who don't have much 
education simply decide not to work.

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So let's set a barrier here,

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so no one above this point 
actually provides us data,

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or below this point.

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So if we eliminate that data here, what 
will happen to our regression estimates?

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There are two things that will happen.

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First of all, all the regression 
results will be biased,

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because now we are fitting the 
regression analysis to this data here,

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and we are cutting this data, these observations,

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that produce negative residuals,

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these are negative residuals because they 
are mostly below the regression line,

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so we have negative residuals 
here and positive residuals here,

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that are included,

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then it pulls the regression line up,

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so the regression results will be biased.

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Then we have no idea of what's the effect 
like in this group with low-income people,

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low education people here,

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and also for those people 
for whom we have the data,

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then we have biased results.

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So if our sample is selected systematically based on the variable that we study,

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then our results will be biased,

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that the magnitude of the bias 
can be great in some instances.

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So this is not just an academic concern,

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I will next demonstrate a couple of examples.

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So there is this a widely known business 
book called Good to Great by Jim Collins.

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And it has sold millions of copies and 
provided inspiration for lots of managers,

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also, it received great attention in Finland,

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when it was first translated to Finnish.

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So many people think this is a valuable book.

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And how was the book written?

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Well, there is a slight problem,

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it's presented as an academic 
study and it kind of is

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but there are methodological 
problems with this book.

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So in the book, they basically chose 
a large number of good companies,

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and they followed, based on 
some accounting measures,

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they followed the performance of those 
companies for 40 years with the research team,

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and then they found 11 companies 
that were initially good companies,

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and then they became great companies,

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according to the definitions 
that these authors here use.

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Jim Collins is the first author but he had a 
team of researchers helping him writing the book.

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So they chose 11 companies 
that perform extremely well

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and then they studied,

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what made those companies perform that well.

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Then they asked later on,

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why did these companies 
perform better than others?

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And then they wrote a book about it.

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So the problem with that is two things.

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First of all, if you choose companies 
that happen to be great in the past,

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then you're sampling on the dependent variable.

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And if a company happens to 
be good, for a chance reason,

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it will get selected,

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or at least some of these companies could 
get selected because of chance reasons.

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And then, when some other researchers 
looked at these companies later on,

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the next 15 year period,

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only one out of the eleven remained great.

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So we can just attribute, the chose of these eleven companies to chance explanation.

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Also what happens is that,

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when a company's performing well,

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then people start to attribute that performance to something that the companies did.

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So that's called the halo effect.

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And when you identify 
companies that are doing well,

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and then you ask those people to evaluate,

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why are these companies doing well,

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then people answer 'well they're doing well because of something that they did in the past'.

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And it's also possible that these 
companies just happen to be lucky,

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and the fact that only one out of eleven stayed great after the 15-year period under study

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just underlines the point that 
that's the likely explanation.

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So these happen to be great for reasons unknown

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and then people attribute that greatness 
to something that the companies did.

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So this sign does not provide 
evidence of causality.

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Let's take another example,

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this is from Morgan and Winship 
book on causal inference.

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And they have this hypothetical college,

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where entry to the college 
depends on the SAT exam,

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the American high school exit exam basically,

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and a motivation score that is measured somehow.

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Motivation score and SAT score are weakly 
and positively dependent on each other,

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and college entry depends on both of them.

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So here is the data, and here's the SAT 
score and here is the motivation score.

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And these guys here were not accepted to the 
college and these circle guys were admitted.

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So the sum of the SAT score and sum 
of their motivation scored determines,

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who gets to go to this hypothetical college.

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So there's a weak positive relationship,

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we can't really see it here, 
but it's around 0.1 correlation,

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but it's not visible to the plain eye.

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What happens if we measure the correlation only from those people who got admitted to the college?

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We only observed students who got to the college,

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there is a strong negative correlation.

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So we get a strong negative correlation,

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because we only studied those 
people who got admitted.

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So if you were the principal of this college,

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a smart principal would ask that does that 
result replicate also on those students

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who didn't get accepted, and 
they find that yes it does,

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so you will get the same negative result.

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This negative result has very 
little to do with the actual  

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relationship between motivation and SAT score,

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instead, it's a function of 
how we selected the sample.

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If we choose the sample so that,

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the sum of motivation and sum of SAT score must be more than a threshold or less than a threshold,

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then you will get this kind 
of negative correlation

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just because of their selection effect.

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So this is called the selection effect 
and the outcome is selection bias.

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So whenever you take a sample,

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unless you are careful that your sample is  

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actually a random sample of 
the population under study,

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then you risk having a 
selection bias in your analysis

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and the bias can be great.

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Let's take another really practical example.

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So I went to the building fair 
in Vantaa a couple of years ago

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and there was this construction company 
presenting an idea called a container home.

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So it's a small home, the 
size of a shipping container

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and these can be built as condominiums.

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So the idea is that you can increase the density of housing by having these very small apartments.

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And then they wanted to get feedback on the idea.

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So how was the feedback collected?

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So they had a polling station,

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where you could indicate whether you 
agree or disagree with the idea that

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this container home is a good idea.

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And how it was actually set up is that,

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you walk along the road here and the 
container home was on the side of the road,

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so you could choose to just walk by,

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or you could choose to go in.

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Then you went in here, you went 
through the apartment to the balcony,

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and that's where the polling station was.

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So what is the problem, why could 
that produce a selection effect?

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Of course, people who are not interested at all,

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who think this is a stupid idea,

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they will just walk past the container home

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and they will never see the polling 
station, which is behind the container home.

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So you actually have to show enough 
interest to go through the container home,

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walk all the way through to the behind,

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and then after you have seen the 
home, then you present an opinion.

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The counter-argument for 
this selection bias is that,

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you only want to have people who have 
actually seen what it looks inside.

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But that's not as important as is the fact that,

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people who think it's a stupid idea in  

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the first place will just walk 
by without providing any data.

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So this is an introduction to issues 
that are related to sampling,

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and there are multiple different 
techniques that you can apply.

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These selection effects can be modelled,

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and also you can do sampling in many 
different ways to increase your efficiency,

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and to avoid the risk of selection bias.

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There are other sampling techniques,

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if you are a Stata user, the Stata has 
a separate user manual for survey data

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that discusses different sampling designs,

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and here are some references 
that you may be interested in.

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The typical sample in a statistical 
book is a random sample,

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and that is also what I will 
be covering on this course,

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because assuming that the sample 
is random simplifies things a lot.

00:16:43.470 --> 00:16:46.530
The second kind of sample that is very common,

00:16:46.530 --> 00:16:48.300
is a cluster sample.

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So cluster sample refers to a sample,

00:16:51.360 --> 00:16:55.350
where the observations are no longer 
equally likely to be selected.

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So random sample is defined as a sample,

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where each observation in a population 
is equally likely to be selected.

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A cluster sample, on the other 
hand, refers to a scenario,

00:17:05.550 --> 00:17:10.020
where you, for example, have to 
interview people at their homes.

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So if you do that and you 
take a sample of let's say,

00:17:15.720 --> 00:17:19.740
all Finnish people, a random 
sample from all Finnish households,

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then you will have to travel all 
over Finland to get your data.

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So in practice, we choose a couple of cities 
and from those cities a couple of streets,

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and we then sample people from those streets or just interview everyone on those streets.

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So we take samples from clusters.

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So if your neighbours are interviewed,

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then it's more likely that 
you are interviewed as well.

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So the probability of being selected is clustered.

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So that if you live close to those people 
who are more likely to be selected,

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you're a lot more likely to be selected as well.

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And that cluster sample causes some 
problems that we'll talk later.

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One way that we can deal with cluster 
sampling is called a stratified sample,

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a stratified random sample.

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Stratified random sample concerns situations,

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where you have for example uneven distribution of people or you have the cluster sample issue.

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Let's say we have a school with 300 
students out of which 30 are minorities.

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In that kind of scenario, taking 
a random sample of 50 students

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is going to likely produce you a very 
small number of minority students.

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So it makes sense to take a sample 
separately from the minority students,

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and sample separately from the other students,

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so that you can get a sample 
that is better for your study.

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So stratification refers to,

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first dividing the sampling frame into 
different strata or different sets,

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and then you take a random sample for each set.

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And stratification improves the 
distribution of your variables,

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it produces random samples that 
can be better in some instances,

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and that's a very commonly used sampling design.

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So these are the three most 
commonly used sampling designs.

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Random sample, everybody is 
equally likely to be selected.

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Cluster sample means you choose 
people from certain areas,

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which you choose in advance,

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so the people in other areas have 
a zero chance of being selected,

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so that's cluster sampling.

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And stratified random sampling means that you divide your sampling frame into different strata

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based on criteria, for example,

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race, education level and so on,

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and then you take a random sample 
of each of those strata separately,

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and that provides you with 
some statistical benefits.

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Then we have the fourth type of commonly used sample called the convenience sample.

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And convenience sample is 
none of these, none of that.

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So convenient sample is something 
that we just happen to get.

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In most cases, if you do a survey 
study and you send out invitations,

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the people or organizations that you 
choose to invite may be a random sample,

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but in the end, those that you get data for is not a random sample of those who got the invitation,

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rather it's a convenience sample,

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just the companies that we happen to get.

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Convenience samples are debated to some extent.

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Some people argue that they should be avoided,

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some people argue that 
convenience samples are useful,

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because they allow us to do designs that wouldn't be possible with random samples for example.

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But you have to understand 
these different concepts

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to understand issues that relate to 
sampling, that I'll cover in later videos