The Manga Guide to Statistics

Amount spent

on makeup (¥)

Amount spent

on clothes (¥)

Ms. A

Ms. B

Ms. C

Ms. D

Ms. E

Ms. F

Ms. G

Ms. H

Ms. I

Ms. J

3,000

5,000

12,000

2,000

7,000

15,000

5,000

6,000

8,000

10,000

7,000

8,000

25,000

5,000

12,000

30,000

10,000

15,000

20,000

18,000

Respondent

St

re

et

sur

vey!

Monthly Expenditures on Makeup and Clothes

Ten ladies in their 20s answered

1. Coelation coeicient

Oh, here is a survey on

makeup expenditures

and clothes

expenditures.

Why don't you

make a chart

first.

Obviously, people who

spend more on makeup

spend more on their

clothes as we.

Then, why don't

we try figuring

out the degr

of relationship?

Yes, sir!

Both

variables

are

numerical!

Scaer chart of monthly Expenditures on

makeup and clothes

Amount spent on Clothes (¥)

Amount spent on makeup (¥)

116 Chapter 6

30,000

20,000

10,000

0

0 10,000 20,000 30,000

Index Formula

Correlation

coefficient

Correlation

ratio

*

Cramer’s

coefficient

*

Numerical and

numerical

Numerical and

categorical

Categorical and

categorical

interclass variance

intraclass variance + interclass variance

−1 – 1

0 – 1

0 – 1

Value

range

*

See page 121, “Correlation Ratio,” and page 127, “Cramer’s Coefficient.”

Data types

the total number of values ×

(min{the number of lines in the cross tabulation, the number of rows in the cross tabulation} − 1)

χ

0

2

Sxy

Sxx × Syy

=

∑

(x – x)(y – y)

– –

∑

(x – x)

2

×

∑

(y – y)

2

– –

√

√

There are

dierent types

of indexes

aording to

the types of

data.

I can s

that.

Because they are both numerical

This freaks

me out!

Here we go!

The index we'

use for makeup

expenditures

and clothing

expenditures is

the coelation

coeicient

.

Take your

time and

calculate it.

3,000 7,000 -4,300 -8,000 18,490,000 64,000,000 34,400,000

5,000 8,000 -2,300 -7,000 5,290,000 49,000,000 16,100,000

12,000 25,000 4,700 10,000 22,090,000 100,000,000 47,000,000

2,000 5,000 -5,300 -10,000 28,090,000 100,000,000 53,000,000

7,000 12,000 -300 -3,000 90,000 9,000,000 900,000

15,000 30,000 7,700 15,000 59,290,000 225,000,000 115,500,000

5,000 10,000 -2,300 -5,000 5,290,000 25,000,000 11,500,000

6,000 15,000 -1,300 0 1,690,000 0 0

8,000 20,000 700 5,000 490,000 25,000,000 3,500,000

10,000 18,000 2,700 3,000 7,290,000 9,000,000 8,100,000

73,000 150,000 0 0 148,100,000 606,000,000 290,000,000

7,300 15,000

Amount spent

on makeup (¥)

Amount spent

on clothes (¥)

Ms. A

Ms. B

Ms. C

Ms. D

Ms. E

Ms. F

Ms. G

Ms. H

Ms. I

Ms. J

Sum

Mean

x y x – x y – y (x – x)

2

(y – y )

2

(x – x)(y – y)

– – – –

– –

x

–

y

–

Sxx Syy Sxy

The proce for calculating the coelation coeicient

for monthly expenditures on makeup and clothes

Let's Lk at the Relationship betwn Two Variables 117

Ack!

Index Formula

Correlation

coefficient

Correlation

ratio

*

Cramer’s

coefficient

*

Numerical and

numerical

Numerical and

categorical

Categorical and

categorical

interclass variance

intraclass variance + interclass variance

−1 – 1

0 – 1

0 – 1

Value

range

*

See page 121, “Correlation Ratio,” and page 127, “Cramer’s Coefficient.”

Data types

the total number of values ×

(min{the number of lines in the cross tabulation, the number of rows in the cross tabulation} − 1)

χ

0

2

Sxy

Sxx × Syy

=

∑

(x – x)(y – y)

– –

∑

(x – x)

2

×

∑

(y – y)

2

– –

√

√

Now, aign the

values to the

formula.

It's easy if you

have a calculator.

The coelation

coeicient

is...0.9680!

The coelation

coeicient gets

closer to ±1 if the

linear relationship

betwn the

two variables is

stronger.

As the

relationship gets

weaker, it gets

closer to 0.

The result I just

calculated is quite close

to 1, so that implies that

makeup expenditures and

clothing expenditures are

very closely related.

That's

interesting.

You are quite

coect.

That would haen if the

clothing expenditures fe

as the makeup expenditures

rose.

When does it get

close to -1?

118 Chapter 6

Sxy

S × S

290,000,000

148,100,000 × 606,000,000

0.9680

negative

coelation

coelation coeicient

arox. -1 arox. 0.5

arox. 1arox. 0

zero

coelation

positive coelation

If the coelation

coeicient is positive, as in

this case, we say, "there is a

positive coelation," and if

it is negative, we say, "there is

a negative coelation."

If it is 0, we say

that "they are

uncoelated."

I understand

completely.

Now,

about the

coelation

coeicient...

Unfortunately, there are

no statistical standards

to aure you that the two

variables have a strong

relationship.

What an

unreliable

index...

Let's Lk at the Relationship betwn Two Variables 119