The Manga Guide to Statistics

Informal Standards of the Coelation Coeicient

Absolute value of the

correlation coefficient

Detailed description

Very strongly related

Fairly strongly related

Fairly weakly related

Very weakly related

Rough description

Related

Not related

1.0–0.9

0.9–0.7

0.7–0.5

Below 0.5

�

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Just for your

information,

informal standards

are given above.

Warning

For example, the two variables are obvi-

ously related in this chart. However, the

correlation coefficient is almost 0 because

the relationship is non-linear.

I mentioned earlier that the correlation coefficient is an index that

shows the degree of

linear relation between two numerical variables.

sample of data unsuitable for

coelation coeicient

Coelation coicient = -0.0825

Oh...

120 Chapter 6

Street Survey in Everyhills

Age and Favorite Fashion Brand

27

33

16

29

32

23

25

28

22

18

26

26

15

29

26

Age

Theremes

Channelior

Bureperry

Bureperry

Bureperry

Bureperry

Bureperry

Bureperry

Channelior

Channelior

Channelior

Channelior

Theremes

Theremes

Theremes

Brand

Ms. A

Ms. B

Ms. C

Ms. D

Ms. E

Ms. F

Ms. G

Ms. H

Ms. I

Ms. J

Ms. K

Ms. L

Ms. M

Ms. N

Ms. O

Respondent

2. Coelation Ratio

On we go!

They have also

surveyed age

and favorite

fashion brand!

That's

numerical

and

categorical.

For numerical data and

categorical data, we use the

coelation ratio.

Its value is...Betwn 0 and 1.

Is the relationship

stronger if the value is

closer to 1 in this case,

t?

Yes, it is.

Let's Lk at the Relationship betwn Two Variables 121

I wi re-

organize the

table.

Hm.

Next, let's

make a

chart.

Wow! It sms

like there

are certain

coelations.

At this point, let’s

actuay calculate

the value of the

coelation ratio.

A right,

let's do it!

favorite fashion brand and age

Scaer chart of

favorite fashion brand and age

Sum

Mean

Theremes Chaelior Burepey

Theremes Chaelior Burepey

122 Chapter 6

Step 1

Do the calculations in the table below.

Step 2

Calculate the intraclass variance (S

TT

+ S

CC

+ S

BB

= how much the data within each category varies).

The value of the correlation ratio can be calculated by following steps 1

through 4 below.

(23 − 26)² = (−3)² = 9

(26 − 26)² = 0² = 0

(27 − 26)² = 1² = 1

(28 − 26)² = 2² = 4

(25 − 29)² = (−4)² = 16

(26 − 29)² = (−3)² = 9

(29 − 29)² = 0² = 0

(32 − 29)² = 3² = 9

(33 − 29)² = 4² = 16

(15 − 21)² = (−6)² = 36

(16 − 21)² = (−5)² = 25

(18 − 21)² = (−3)² = 9

(22 − 21)² = 1² = 1

(26 − 21)² = 5² = 25

(29 − 21)² = 8² = 64

(Theremes − average for Theremes)²

(Channelior − average for Channelior)²

(Bureperry − average for Bureperry)²

Sum

14

50

160

S

TT

S

CC

S

BB

S

TT

+ S

CC

+ S

BB

= 14 + 50 + 160 = 224

Let's Lk at the Relationship betwn Two Variables 123

Step 3

Calculate the interclass variance, or how different the categories are from each other.

(number of votes for Theremes) × (average for Theremes − average for all data)²

+ (number of votes for Channelior) × (average for Channelior − average for all data)²

+ (number of votes for Bureperry) × (average for Bureperry − average for all data)²

Step 4

Calculate the value of the correlation ratio.

So...The value of the coelation

ratio for age and favorite fashion

brand is...

4 × (26 − 25)² + 5 × (29 − 25)² + 6 × (21 − 25)²

= 4 × 1 + 5 × 16 + 6 × 16

= 4 + 80 + 96

= 180

180

224 + 180

180

404

= 0.4455

=

interclass variance

intraclass variance + interclass variance

124 Chapter 6