The Manga Guide to Statistics

Wow! Area and ratio and

probability are indd

the same.

I am impreed

that you have

understd

everything.

Am I smart

or what?!

Don’t forget. This

relationship of

area = ratio = probability

can be alied to any

probability density

function—Not just

the standard normal

distribution.

I surely

won’t.

Would you like me

to introduce you to

another probability

density function?

I’m ready

for it!

98 Chapter 5

We say, “x foows a chi-square distribution with

n degrs of frdom (df)” in statistics.

4. Chi-square Distribution

There is a kind

of distribution

caed the

chi-square

distribution.

“chi?” Is

that like

a square

Kayak?

Don’t woy. You’

never have to learn

this formula itself

unle you become a

mathematician.

*bad joke...

No,

it wasn’t

so bad!

What a

complicated

formula...

YOU

are

SO

MEAN.

I just showed

it to you to

scare you.

To begin with,

let me show you

graphs with 2, 10,

and 20 degrs

of frdom.

It’s geing even

more diicult!

*

When the probability density function is...

When

x › 0...

ƒ(x) =

2

df

2

1

e

–x

dx

× ∫

∞

x

0

− 1

df

2

× x × e

x

2

−

− 1

df

2

When

x ≤ 0...

ƒ(x) = 0

Let's Obtain the Probability 99

The shape of

the graph varies

aording to the

number of degrs

of frdom.

2 degrs of frdom

10 degrs of frdom

20 degrs of frdom

100 Chapter 5

BANG!

By the way, I

have no idea

what “degrs

of frdom”

are.

Oh, excuse me

for failing to

explain that.

What was the name for

a in the simple function

f(x) = ax + b?

Hm...Was it

the slope?

Very gd! If the

value of a changes,

the slope of the

graph wi change.

We can take that for

granted, can’t we?

YES.

Degrs of frdom are

just like the slope. The

value aects the shape of

a probability distribution

function.

In other words, when

the value of degrs

of frdom changes,

the shape of the graph

changes as we.

Is

that a

“degrs

of

frdom”

means?

It's also

related to

sample size.

The bier the

sample, the

more degrs

of frdom.

Let's Obtain the Probability 101

Just like there is a table

of probabilities for

the standard normal

distribution,

There is a table of

probabilities for the

chi-square distribution.

The table of

chi-square

distribution is...

A table that shows the value of

χ², which is a graduation on the

horizontal axis that coesponds

to the probability (which we know

is equivalent to the area and ratio)

of this part p.

102 Chapter 5