The scope of inference in statistical studies hinges on two crucial factors: random sampling and random assignment. Understanding these allows researchers and consumers of research to correctly interpret study results, determining whether conclusions can be generalized to a larger population or if cause-and-effect relationships can be established.
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all right so we're gonna close out our
chapter this is the
last lesson of chapter four and we're
closing it out by talking about just a
couple topics that are really
important in terms of realizing what you
can do
and what you can't do with the results
you get from a study
so this first slide right here talks
about a huge
topic really really important topic that
you need to
understand very well called scope
of inference scope of inference is one
of those things that
after you leave my class after you go on
to be an adult
hopefully this is a topic that you will remember
remember
because it really really matters in
terms of what you can do
with results that you get from a study
and it's something that the average
adult doesn't understand well enough
and it's something that if you're
reading articles online or different things
things
about just studies that you see people
who write articles
frequently mess this topic up and misapply
misapply
the scope of inference and study so i
have a little bit of a table here at the
bottom i'm going to go ahead and delete
that though
i can't delete it right now but instead
of filling out this table what i'm going
to do is have you guys write down
just the key points of scope of
inference off on the side somewhere in
your notes
there are two things that we are
concerned about
with regards to scope of inference we
care about whether or not our data came
and we care about whether or not we had random
random
assignments these two
factors are what you need to consider
in order to decide what you can do with
your results
random sampling from a population means
that you pulled your sample randomly
out of the entire population everybody
within that population
had a chance to be chosen for your study
if you randomly sample
you can apply your results to that
entire population
if i take a random sample of adults in
st louis
i can apply the results from those
adults to the entire
population of saint louis couldn't apply
it to the rest of the u.s
because i didn't sample from the rest of
the u.s those people didn't have a
chance of being chosen
so random sampling allows you to make
inference about
the population inference means basically
making predictions and stuff like that
so random sampling allows you to talk
about the population
all right random assignment on the other hand
hand
is when you break people up and you
create roughly equivalent groups and experiments
experiments
so if you have roughly equivalent groups
due to random assignments
and you see a difference between those
two groups
you can assume that that difference was
because of the variable that you manipulated
manipulated
random assignment allows you to make conclusions
conclusions
or inferences about cause
so if you want to say that one variable
causes another one
it has to be in experiments where you
have random assignments
if you want to talk about the population everybody
everybody
you need to have random sampling most experiments
experiments
that you see in here about are not able
to be applied to the whole population
why is that well for experiments when
you're talking about some college
research lab or something like that
they don't randomly pick people out of
the population and be like you you're
coming to be in my study i selected you randomly
randomly
most experiments rely on volunteers or
people who sign up to be in the studies
right there
so those people that are volunteers are
probably not representative
of the population as a whole first off a lot
lot
of people who are like subjects in
experiments are college students
they're a very common audience right
there because they're in a university
anyway they can get extra credit in
their classes maybe get a little extra money
money
so a lot of experiments who are
performed on college kids
they're typically younger healthier than
the average person in our population
so we can't apply the results that we
see in college kids
to the rest of the population if we're
taking some group that's like high
cholesterol risk and we're doing an
experiment on them
we can only talk about how this drug
works in people with high cholesterol
like the ones in the study so the
disclaimer you usually see in experiments
experiments
is that the results can be applied we
can determine that this medication
caused the benefits or the whatever but
we can only apply it to people like
those in the study so it's like a little
disclaimer in most experiments that you
will see
so what this table is doing is just
summarizing what i've been talking about
right here
were they randomly selected were they
randomly assigned
if you are randomly selected that means
that you
can make inferences about the population
okay so were they randomly selected yes
yes you can talk about the population
yes you can talk about the population
if they are not randomly selected that
means that you cannot talk
about the population were they randomly assigned
assigned
treatments if yes then you can
talk about cause and effects and if no
you cannot talk about cause and effects
so you can see it parenthetically right here
here
most experiments fall into this group
you can't make inferences about the
population because they're mostly
volunteers for the study
but you can talk about cause and effects
a lot of observational studies fall over
here where there was a random sample you
can talk about the population
but you can't talk about cause and fact
flashback to one of our earlier lessons
where we looked at smoking compared to
adhd rates in children
that wasn't an experiment so what we
could say
in that context is that it appears that
smoking is connected
with higher rates of adhd those two
things go together
and if you smoke you're probably also
going to have a higher risk of having a
kid with adhd
but we can't go that extra step to say
the smoking caused
the rate of adhd to increase because of
confounding factors we don't know what's
actually responsible for it
newspaper articles mess up scope of
inference all the time
you will see studies all the time where
maybe the researcher knew what they were
doing and the researcher didn't do
anything wrong
but some journalist who reads it or some
person who wants to make their buzzfeed
article about whatever
doesn't understand scope of inference so
they incorrectly interpret the results
to say oh this
caused this we'll look at some articles
where that happens in class
so what i have here is just an example
to practice scope of inference here
we're going to test whether listening to
music while you
work um impacts your i think it's going
to be grades
in school gpa at the end of the semester
okay and what i have right here
is four hypothetical designs and we're
just going to talk really quickly these
are pretty easy questions
once you understand scope of inference
where can we apply our results
okay so the following slide right here
is where you can write these down but
i'm just going to do it on the slide so
i don't have to tab back and forth i'm
going to write it right here
okay so we are going to take everybody
in our ap stats class
and we are going to have them be in a
study ask them hey do you guys listen to
music or not and then look at gpa
um at the end of the semester so i let
you guys decide do you listen to music
people who say yeah are in this group
people who say no are in this group end
of semester we would look at them
okay so we did not randomly sample
we used an ap stats class we can't talk
about the whole population
so we can't talk about
only this class so if there is a
difference between
the two groups i can say in this class
kids who listen to music do better or do
worse that would be fair
but i can't apply my results beyond my
classroom because i
didn't randomly sample okay i also
didn't randomly assign you
to groups since you were not randomly
assigned to groups
that means if there's a difference i
can't say it was because of the music
because there could be other confounding
factors like um
maybe kids who like music are
more motivated or less motivated you can
run all those hypotheticals
so we can't talk about cause and effect
either so we can't say
the music caused
a difference the word caused
is a very powerful word in ap stats
don't use it unless you actually have
cause and effect you can talk about
things being
linked together or there being a
connection but mentioning
effect or cause is a really strong
statement that you should not do unless
you were randomly sampling
okay so this is how i would want you
guys to write your answers but i'm going
to write them a lot shorter
in these next couple examples to not
slow things down right here
now in the second scenario we are
randomly sampling from our school
and then we ask if they listen to music
or not and be breaking unity groups
so i did randomly assemble that means i can
can
apply to the population
of my school can't apply beyond my
school because i didn't use people from
other schools
but i can apply to the whole school even
if i don't talk to every single person
but there would be no cause and effects
so i could say the same sort of thing
can't say that music caused a difference
because i just let you establish your
own group same as the first one
all right next up get every nap stats
class so you guys are my captive
audience you're in my study
now i'm going to randomly assign half of
you to each group
random assignments should make it so the
groups are about equal
in all those different factors you can
think about so if there's a difference
i can say it's due to the music so this
but a yes to cause and effect
and then finally on this last one right
here this is like the gold standard it's
a random sample from my school
and i did do random assignments so i
could make conclusions about both
this is generally unrealistic in most experiments
experiments
like i said experiments tend to live
here observational studies
so the last thing i believe i need to
talk about with you guys
oh two things okay first of all this is
an article we're probably going to read
in class but it's kind of interesting
um based on taking vitamins and
the connection that vitamins have with
your overall health
turns out that when you do experiments
where you actually randomly assign
people to take vitamins or knots
there's usually not too much of a
difference in health outcomes
between the two groups vitamins don't
tend to do a lot
in terms of your overall health but
if you do an observational study where
you don't do random assignment you just
look at data
people who take vitamins tend to have
better health outcomes than people who don't
don't
but it's because of confounding factors
if you're taking vitamins you probably
care more about your health you do other
things like exercise diet et cetera
that make you have those better health
outcomes so if you're not
careful you can very easily run into an issue
issue
where those confounding factors make you
think something is causing
a situation when it's actually not
and the very last thing that we have to
talk about in this chapter
it's quick but it's important being ethical
ethical
and collecting your data just something
that we have to talk about here
um because you guys will be running your
own project later on this semester
whenever you collect data you have an obligation
obligation
not to share that data with people
outside your studies and keep things
confidential you have to be upfront with
people you can't lie to your um the
people in your study
and you can't be like oh this person
said this on their survey
and that's just not an okay thing to do
um when you if you actually go into a
career with research and you violate
these principles of ethics you can
actually be like
blacklisted from the um like community
so you can't actually participate in
research further
um all studies if you guys do any like
high level
statistical studies you'll submit them
to a review board and they'll make very
certain that you're not breaking any
guidelines there so use common sense and
common decency
when you guys do your project for me
later this semester
results do need to be kept confidential
so that
is the end of our first unit on experimental
experimental design
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