The Manga Guide to Statistics

Here is a scatter chart of favorite fashion brand and age (when the correlation ratio is 1).

Here is a scatter chart of favorite fashion brand and age (when the correlation ratio is 0).

As explained earlier, the value of the correlation ratio is between 0 and 1.

The stronger the correlation is between the two variables, the closer the

value is to 1, and the weaker the correlation is between two variables, the

closer the value is to 0. Refer to the charts below for more details.

50

40

30

20

10

Channelior BureperryTheremes

Average

correlation ratio is 1  data included in each group is the same  intraclass variance is 0

50

40

30

20

10

Channelior BureperryTheremes

correlation ratio is 0  average for each group is the same  intraclass variance is 0

126 Chapter 6

Unfortunately, there are no statistical standards such as “the two

variables have a strong correlation if the correlation ratio is above a

certain benchmark.” However, informal standards are given below.

The result of the calculation for the case in question was 0.4455,

so the variables are fairly weakly related!

3. Cramer's Coeicient

I wonder if there is a gd

example I can use to explain the

coelation of two categorical

variables.

Let me

s...

How about this?

We Asked 300 high schl

students, "how would you like

to be asked out?"

Informal Standards of the Coelation Ratio

1.0–0.8

0.8–0.5

0.5–0.25

Below 0.25

Correlation ratio

Detailed description

Very strongly related

Fairly strongly related

Fairly weakly related

Very weakly related

Rough description

Related

Not related

�

�

�

�

Let's Lk at the Relationship betwn Two Variables 127

Hm...”my ideal

way of being

asked out is

phone, e-mail,

face to face”...?

It amazes me what kind

of weird stu is in

girls' magazines.

It's

not

weird!

Cro tabulation of sex and desired way of being asked out

Cro tabulation of sex and desired way of being asked out

(horizontal percentage table)

desired way of being asked out

desired way of being asked out

phone

e-mail

face to face

phone

e-mail

face to face

A table that

joins two

variables

like this one

is caed

a cro

tabulation.

sex

female

male

sum

sum

sum

sex

female

male

sum

This indicates that 74 out of 152 males answered that they’d like to be asked out directly.

Interesting...Girls tend

to prefer being asked

out by e-mail,

But boys tend to

want to be asked out

directly.

This shows that 49% ( × 100) of the 152 males would like to be asked out directly.

74

152

128 Chapter 6

This would make

a gd example.

34

38

72

61

40

101

53

74

127

148

152

300

23%

25%

24%

41%

26%

34%

36%

49%

42%

100%

100%

100%

It indd sms that

there is a dierence

in the desired way

of being asked out

betwn girls and

boys.

In other words, there is a

coelation betwn sex

and desired way of being

asked out.

I should

contact

mr. Igarashi

directly if I

am going to

ask him out...

Rui? Are you

listening?

Sure,

I am.

What was the

index to expre

the degr of

coelation

betwn two pieces

of categorical

data?

The Cramer's

coeicient!

The Cramer's

coeicient is also

caed the cramer's v

or an independent

coeicient.

I caot cram

so much new

vocabulary

into my head!

We, that

was kind of

fuy.

* Bad joke again...

You don't have

to be nice to me.

*

Let's Lk at the Relationship betwn Two Variables 129

Step 1

Prepare a cross tabulation. The values surrounded by the bold frame are called actual measurement

frequencies.

Step 2

Do the calculations in the table below. The values surrounded by the bold frame are called expected

frequencies.

The Cramer’s coefficient can be calculated by following steps 1

through 5 below.

Sum

Sex

Female

Male

Sum

Phone E-mail Face to face

Desired way of being asked out

34 61 53 148

38 40 74 152

72 101 127 300

Sex

Female

Phone E-mail Face to face

Sum

Male

Sum

Desired way of being asked out

148

152

72 101 127 300

148 × 72

300

152 × 72

300

152 × 101

300

152 × 127

300

148 × 101

300

148 × 127

300

sum of male × sum of face to face

total number of values

Formula A

130 Chapter 6