Leseprobe
Fresh up your knowledge
Correlation
Fresh up your knowledge
Correlation
· In easy words:
Correlation
describes how two variables are
In easy words:
Correlation
describes how two variables are
determined by each other and how a change in one of them
affects the other
affects the other
· A crude measure of the relationship between variables is
covariance
covariance
· We can measure the relationship between two variables using
l i
ffi i
correlation coefficients
3
Why should correlation be interesting?
Why should correlation be interesting?
Let's use an easy example:
Let s use an easy example:
Imagine you have created a TV-advertisement for an already
existing sport drink called "BLUECOW" and your boss is asking
existing sport drink called BLUECOW and your boss is asking
you if your spot benefits the numbers of sold drinks. How can you
find out if it does or if it's crap?
Answer:
Answer:
You measure the correlation between the adverts and the
numbers of sold drinks
numbers of sold drinks
4
Do you still know anything about correlation from
h
the statistics course?
· The correlation coefficient has to lie between
-1
and
+1
.
ff
f
f
l
h
· A coefficient of
+1
indicates a
perfect positive relationship
,
· So a coefficient of
1
indicates a
perfect negative relationship
· So a coefficient of
-1
indicates a
perfect negative relationship
,
· And a coefficient of
0
indicates
no relationship
at all.
p
5
How to interpret the values
How to interpret the values
The correlation coefficient is a commonly used measure of the
The correlation coefficient is a commonly used measure of the
size of an effect.
· Values of
± 1
represent a
small effect
· Values of
± .1
represent a
small effect
,
·
± .3
is a
medium effect
and
·
± .5
is a
large effect
.
However, focus on the context of your research to interpret the
,
y
p
values instead of simply following these benchmarks.
6
Starting slowly
Covariance
Starting slowly
Covariance
cov(x,y) = [SUM (x
i
- x
mean
)(y
i
- y
mean
)] / n - 1
with n = number of value pairs
with n number of value pairs
x
mean
= [SUM (x
1
+x
2
+...x
n
)] / n of x-values
y
mean
= [SUM (y
1
+y
2
+...y
n
)] / n of y-values
7
Starting Slowly
Covariance Example
Starting Slowly
Covariance Example
Participant
1
2
3
4
5
Mean
s
Adverts watched
5
4
4
6
8
5.4
1.67
BlueCow cans
bought
8
9
10
13
15
11.0
2.92
cov(x,y) = [SUM (x
i
- x
mean
)(y
i
- y
mean
)] / n - 1
cov(x,y) = [SUM (-0.4)(-3) + (-1.4)(-2) + (-1.4)(-1) + (0.6)(2) + (2.6)(4)] / 5 1
cov(x,y) = [1.2+2.8+1.4+1.2+10.4] / 4
(
)
/
cov(x,y) = 17 / 4
cov(x,y) = 4.25
A positive value shows that if one variable increases, the other increases as well.
A positive value shows that if one variable increases, the other increases as well.
A negative value shows that if one variable increases, the other decreases.
8
Covariance
Standardization
Covariance
Standardization
The value of
covariance
alone is not really objective and comparable, so
we need to
standardize
it by using the
standard deviation (s
x
, s
y
)
to
receive
Pearson's correlation coefficient
.
r = cov
xy
/ s
x
s
y
"Th
P
'
l ti
ffi i
t
i
t i
t ti ti
d
"The
Pearson's correlation coefficient
is a parametric statistic and
requires interval data for both variables. To test its significance we can
assume normality, too."
9
Source: Field, A., Miles & Field, Z. (2012)
Covariance Example
Pearson's correlation
Covariance Example
Pearson s correlation
Participant
1
2
3
4
5
Mean
s
Adverts watched
5
4
4
6
8
5.4
1.67
cov(x,y) = 4.25
r = cov
xy
/ s
x
s
y
BlueCow cans
bought
8
9
10
13
15
11.0
2.92
cov(x,y) 4.25
s
x
= 1.67
s = 2 92
r cov
xy
/ s
x
s
y
r = 4.25 / 4.88
r = 0 87
s
y
= 2.92
s
x
s
y
= 4.88
r = 0.87
10
Remember this slide?
Remember this slide?
· The correlation coefficient has to lie between -1 and +1.
· A coefficient of +1 indicates a perfect positive relationship,
· So a coefficient of -1 indicates a perfect negative relationship,
· And a coefficient of 0 indicates no linear relationship at all.
Answer to our example:
A Pearson's correlation coefficient,
r = 0.87
, shows a strong
positive relationship between the "BlueCow" ads and bought
"Bl
C
"
"BlueCow" cans.
11
Face new problems:
Causality
Face new problems:
Causality
· Direction of causality:
No statistical reason why we shouldn't be able to interpret the
variables in the opposite way.
For example:
The number of cans somebody is buying affects the number of adverts he or
h i
i
she is seeing.
· Third-variable problem:
Normally there is more than one reason why we start buying / doing
something, and these unmeasured variables affect the results as
well.
12
Ende der Leseprobe aus 18 Seiten
- Arbeit zitieren
- Kersten Thiele (Autor:in), 2018, Discovering Statistics Using R-Correlation, München, GRIN Verlag, https://www.grin.com/document/430073
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