Materi Analisis Data Kategori

Exact Test

Exact Test

Exact Tests

Exact Tests

Favorable

Favorable

Unfavorable

Unfavorable

Total

Total

Test

Test

Control

Control

10 2

10 2

2

2

4

4

12

12

6

6

Total

Total

12 6

12 6

18

18

►

A test treatment

A test treatment

and a control are

and a control are

compared to determine whether the rates of

compared to determine whether the rates of

favorable response are the

favorable response are the

same.

same.

►

T

T

he sample sizes requirements for the chi-

he sample sizes requirements for the

chi-square tests are not met by these data

►

if you can consider the margins (12, 6, 12, 6)

if you can consider the margins (12, 6, 12, 6)

to be

to be

fixed, then you can assume that the

fixed, then you can assume that the

data are distributed hypergeometrically and

data are distributed hypergeometrically and

write

write

►

Pr

Pr

(

(

n

n

_ijij

)

)

=

=

n

n

₁₊₁₊

!n

!n

₂₊₂₊

!n

!n

₊₁₊₁

!n

!n

₊₂₊₂

!

!

/

/

n!n

n!n

₁₁₁₁

!n

!n

₁₂₁₂

!n

!n

₂₁₂₁

!n

!n

₂₂₂₂

!

!

►

p-value is the probability of the observed

p-value is the probability of the observed

data or more extreme data occurring

data or more extreme data occurring

under

under

the null hypothesis

the null hypothesis

►

With Fisher’s exact test, determine the

With Fisher’s exact test, determine the

p

p

-

-value for this table

value for this table

by summing the

by summing the

probabilities of the tables that are as likely or

probabilities of the tables that are as likely or

less likely, given the fixed

The following table includes all possible table configurations and their

The following table includes all possible table configurations and their

associated

associated probabilities.probabilities.

Table CellTable Cell

► _{(1,1) (1,1) (1,2) (1,2) (2,1) (2,1) (2,2)(2,2) Probabilities Probabilities}

---► _{12 12 0 0 0 0 6 6 0.00010.0001} ► _{11 11 1 1 1 1 5 5 0.00390.0039}

---► _{1010 2 2 2 2 4 4 0.05330.0533}

---► _{9 9 3 3 3 3 3 3 0.23700.2370} ► _{8 8 4 4 4 4 2 2 0.40000.4000} ► _{7 7 5 5 5 5 1 1 0.25600.2560} ► _{6 6 6 6 6 6 0 0 0.04980.0498}

To find the one-sided

To find the one-sided pp-value, you sum the probabilities as small or smaller -value, you sum the probabilities as small or smaller than those

than those computed for the table observed, in the direction specified by computed for the table observed, in the direction specified by the one-sided alternative. In

the one-sided alternative. In this case, it would be those tables in which this case, it would be those tables in which the Test treatment had the more favorable

►

To find the two-sided

To find the two-sided

p

p

-value, you sum

-value, you sum

all of the probabilities that are as small

all of the probabilities that are as small

or smaller

or smaller

than that observed, or

than that observed, or

►

p = 0

p = 0

.

.

0533 + 0

0533 + 0

.

.

0039 + 0

0039 + 0

.

.

0001 +

0001 +

0