The Manga Guide to Statistics

1. hypothesis Tests

Now,

today's

leon is...

Hey! Don't you have

anything to say?

TAH-RAH!

We, we, excuse

me for not

noticing. Is that

your new uniform

you were talking

about the other

day?

Yeah! This is sti a

trial product, but I

am showing you as

a special favor.

We, thank you...

You lk gd

in it.

Thanks.

So, what

is today's

leon?

Remember learning

about the Cramer's

coeicient in our last

leon?

You mean that

survey on how

to ask out

someone?

In that example, the

cramer's coeicient

was 0.1634, And the result

turned out to be very

weakly coelated.

Yes, I remember

that.

Now, think

carefuy,

Rui.

The result of that survey

was obtained from the

responses of 300 people...

...Who were chosen

randomly from a

high schl students

residing in japan.

If a dierent 300

people were chosen,

the cramer's coeicient

would not have bn

0.1634.

Come to think of it,

you are right.

*We asked 300 high schl

students, "how would you

like to be asked out?"

*

Let’s Explore the Hypothesis Tests 145

Do you have any idea

what the value of the

cramer's coeicient

for the population

of this example, a

high schl students

residing in japan,

would be in the first

place?

How am I

suosed to

know that?

That's a natural reaction.

Unfortunately, no one

knows, because it is

impoible to ask this

question of every single

student in Japan.

Uh-huh.

It is not only in

this example that

you caot get the

cramer's coeicient

for the population. It is

generay impoible in

a cases.

That is why

we Have no

choice but

to...

146 Chapter 7

make an

informed

decision about

the cramer's

coeicient,

such as,

"Since the cramer's coeicient obtained

from my random sample of 300 people

is 0.1634,

The cramer's coeicient

for the population must be

something like that."

That's not as

convincing as

I thought.

I bet there is a way

to do something

About it using

statistics as in

other cases.

Even if you make fu use

of statistics, the precise

cramer's coeicient for

a population Wi never

be obtained, because it’s

impoible to survey

every single member

of the population. So...

soy to disaoint

you, but no.

No?!

Let’s Explore the Hypothesis Tests 147

However, there is a way

to find out if...

...the cramer's coeicient

for a population is not

zero!

Of course it's a big

deal. It gives you an

objective view about

the population.

It Doesn't sm like

a big deal to me.

How do you

do it?

I have mentioned in our

previous leon that

we wi study tests of

independence today. This is

the means of analysis we

are going to use now.

No, no, it’s

completely

dierent.

Is that something

like the test

of english

proficiency?

A test of independence

is a kind of analysis

technique that is

generay refeed to

as a hypothesis test in

statistics.

Let me explain

hypothesis tests

first.

YES, PLEASE.

Tests Of Independence

Tests Of Coelation

Ratio

Tests Of coelation

Tests Of Dierence Betwn

Population Means

Tests Of Dierence

Betwn Population

Ratios

Hypothesis

Tests

148 Chapter 7