Limits of correlation coefficient - Correlation & Regression, Business Mathematics & Statistics Video Lecture | SSC CGL Tier 2 - Study Material, Online Tests, Previous Year

in this video we're going for some of
the common issues come along with
correlation because it's while it's used
frequently there are is has a lot of
issues statistically to come along with
it so correlation is a very useful
descriptive statistic and inferential
statistic but it has many limitations
first and foremost it cannot be used to
measure differences or causality
remember that can only come from a true
experimental research design where you
have total randomization you have
manipulation and control correlation
only measures relationships or
associations and the researcher is not
going to control any other influencing
or compounding factors so again
researcher does not manipulate
researchers does not control like you
would find in your experimental designs
as a result correlation cannot imply
causality so here as you can see in this
visual we have two different variables
and in those two different variables we
would have maybe up here we have X and
then here we have Y it could be that X
causes Y it could be that Y causes X or
because correlation only looks at
relationships between x and y we don't
know if some other Z variable that we
haven't measured yet has come in and can
replace that factor so we have to
consider that the relationship is
actually being caused by some form of
outside factor a common example you'll
see in textbooks is the relationship
between math content knowledge and shoe
size amongst middle school age
elementary school-age children well
there would be a correlation as those
children's feet get better they know
more math well but is it really the feet
that are in are causing that or in some
outside factor like they're getting
older and therefore they're also taking
more math classes and they're going to
know more about math in
seventh-grade than they do press a
second grade when they have smaller feet
so we cannot imply a cause and effect
the next relation or the next part we've
talked about a few times but I just want
to highlight the point is that
correlation can only measure linear
relationships a zero correlation does
not indicate no relationship because it
cannot rule out a curvilinear
relationship it only rules out a linear
relationship related to this is that you
can have outline scores are going to
potentially increase or decrease values
outliers are a big factor here and only
one outlier can really affect or
influence your outcomes visually this is
a lie you're to see in pictures so if
you look in this picture on the Left we
have a correlation of 0.6 0 that is a
strong or a strong moderate to strong
positive relationship over here but you
notice we have this one outlier and if
you looked in here this doesn't look
like there's much relationship at all if
we remove that one outlier and take it
out
now we look over to the right look at
the way that that relationship is
actually coming out it's actually a very
negative weak relationship same thing
can happen in the opposite direction
we're here we have one outlier it's
pulling our relationship down so that we
have a weak positive relationship as
soon as we remove that outlier now the
relationship goes to a strong positive
relationship so the outlier doesn't
necessarily increase or decrease the
relationship it just can but it can
strongly influence or pull their
relationship in a different direction
notice so why does it drop so
substantially well if the trend we're
truth the outlier implies we would see
curvilinear relationship which are
calculated there's no relationship
because a correlation coefficient can
only assess
a linear relationship so what's
happening is that outlier is starting to
create excuse me bring up the drawing is
starting to create what the computer
thinks is a curvilinear relationship
without or without the dots around here
and that's what's pulling the value down
so much a related but slightly different
issue is what we call divergent groups
so in this case some form of sub
grouping is occurring within your
samples that's influencing either your X
or Y predictor criterion variables as a
result there's the mean difference that
might be influencing the relationship
between X in Y so the question is
whether or not the same relationship
exists between these two two subgroups
again a picture so here I have a
relationship between the amount of
stress as our predictor and I have
salary in dollars and this is a very
sexist example but we have males making
more money than females then we see the
male group being up here and we have the
female grouping up they are down there
it would be a problem if we didn't
actually check to see if males and
females have the same relationship
together because if we looked at this
data separately and chopped it up this
day or that relationship might be
different than that relationship but if
we throw all the data into one study the
correlation might not truly be
presenting our data so what do we do
about here and like a or we want to
determine if a present mean difference
exists between the presence of males and
females so the researcher thinks
divergent groups exist they should run a
t-test which we'll talk about in our
next class and determine if the groups
differ significantly on either variable
if there is a significant difference
than the researcher should calculate two
separate correlations so instead
correlations would look like this where
we have a correlation for female on the
left and correlations for males on the
the final the final limitation we're
gonna discuss is got two names one of
the names is called homogeneity of the
group this is awesome also sometimes
called restricted range homogeneity of
the group if you think about the prefix
of homo means similar so basically the
same as the group is very very similar
or restricted range you're going to see
on you the x value or the Y value a lot
of similarity between your x and y
variables if you limit the range of one
of those variables the correlation is
going to be influenced and typically
it's going to be lowered you can only
the thing is with correlation you can
only extrapolate to the data that you
have within your range so you can't
expand out again visually this makes a
lot more sense so here I have a pretty
small range that I'm working here with
Asian performance where my variables are
only within this small box and I can't
extrapolate out across here or up there
however once I start to move and add
more information across the x and y axis
a clear relationship between x and y
appears and that and you'll see it's a
stronger positive relationship as
opposed to before it was apparent to be
a negative relationship within the box
you can kind of see in here the
relationship here non negative excluding
no no relationship all right that's the
end of this lecture