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>> Getting a representative
sample, it's not easy
and it's not even guaranteed.
And that's why
with inferential statistics,
we can actually never say we
proved a hypothesis as much
as we'd like to.
That is, any time we select
our sample there's always the
possibility
that it might not
be representative.
Now let's say that I decide
to personally pick a sample,
let's say a size one in which
to get an idea
of the typical college student
IQ and so I go ahead
and I pick someone.
It's very possible
that unconscious bias may have
influenced who I picked
or if not this person I picked
this person
or this person here.
Maybe's there something going
on that maybe not even I'm
aware of that's influencing
who I'm picking and so
that is going to get
in the way
of me getting a good
representative sample.
And so if I want a
representative sample
and let's keep
at the most simplest level,
size one.
Then to get rid
of this bias the next best
step up is random selection
where every person would have
an equal chance
of being included
in my sample.
So let's say that I go
with a random selection
of one student to get an idea
of the typical college
student IQ.
We'll say that IQ
of college students is
normally distributed
and for sake of discussion,
we'll go with the mean IQ
of 116 and a standard
deviation of 16.
So with the mean of 116
and a standard deviation
of 16 we have our measure
central tendency right here
to 116 with let's say most
college students right there.
That's our highest frequency.
And as you go
into a higher IQ,
there's fewer students
and as you go further higher
IQs, less students and same
with lower IQs.
Well at what point would we
consider a college student not
representative
of the general
college student?
What point would we say
that person is
not representative?
Let's just say that we put
that at plus
and minus two
standard deviations.
Well, if we go
with that definition
that if you're more
than two standard deviations
above the mean,
you're not representative.
And if you're less
than two standard deviations
below the mean you're
not representative.
We would say if you happen
to randomly pick a college
student whose IQ is between 84
and 148, that student is
at least somewhat
representative
of all other college students.
But that if the college
student's IQ is 148 or more
or let's say like 149,
or if the college student's IQ
is, you know,
83 or some other value here
in the shaded region,
that college student is
not representative.
Well in that case,
what's the probability,
even though we are using
random selection
that our sample size one is
not representative?
To answer that question we
would have to go to a Z table.
A Z table is a table
where you determine how many
standard deviations the value
is away from the mean
and it will give you the area
under the curve
that corresponds.
So 84 is two standard
deviations below the mean
so it's a Z score
of negative two.
148 is two standard deviations
above the mean
and that corresponds
to a Z score of a positive two
because that's one two
standard deviations
above the mean.
So here we're looking
at a Z table
in the shaded area is the
proportion that can be looked
up in the Z table.
And we'll look
up a Z score 2.00.
So here we go.
A Z score of 2.00.
Here's a Z score of 2.00.
That proportion is .023.
That is, it's saying
that shaded area beyond Z
would be .023.
So the proportion of people
that we might randomly pick
who would not be
representative, we have .023
for those people
who are two standard
deviations above the mean.
And we have .023
for those people
who are two standard
deviations below the mean.
If we add up those two
proportions,
the .023 plus .023 our
combined area,
these two red areas,
where we would say someone is
not representative is .046.
That is about 4.6 percent
of the time we might randomly
select someone
who is not representative.
Thus, the probability
of not being representative
as we've defined it here
is .046.
Okay. I hope this helped you
in thinking
about how random selection
does not always give you a
representative sample.
We'll learn more
on how this applies
to larger sample sizes.
Take care.