# Discovering Statistics Using R-Correlation

## Presentation slides, 2018

Excerpt

Correlation
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:
you if your spot benefits the numbers of sold drinks. How can you
find out if it does or if it's crap?
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
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
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
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.
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
Excerpt out of 18 pages

Details

Title
Discovering Statistics Using R-Correlation
College
University of Applied Sciences Ansbach
Course
Wissenschaftliches Arbeiten II
2,0
Author
Year
2018
Pages
18
Catalog Number
V430073
ISBN (eBook)
9783668742819
File size
1330 KB
Language
English
Tags
discovering, statistics, using, r-correlation
Quote paper
Kersten Thiele (Author), 2018, Discovering Statistics Using R-Correlation, Munich, GRIN Verlag, https://www.grin.com/document/430073