meeting 13 One Sample Descriptive Hypothesis Test

07/05/2011

One Sample Descriptive
Hypothesis Test

Two main inferential statistics
tests
Should be normal
distributed
(classical
assumptions tests)
Parametric
Interval and ratio
data

Presented by
Mahendra AN

Inferential
Free classical
assumptions

Nonparametric
Nominal and
ordinal data

Sources:
Sugiyono, Statistika Untuk Penelitian, Alfabeta, Bandung, 2007
Neil Burdess, Starting Statistics a Short, Clear Guide, Sage, 2010

Basic Principles
Popu la t ion
pa r a m e t e r
μ = mean
σ = standard
deviation
ρ = proportion

Degree of freedom Concept
Reduction

St a t ist ic

X = mean
s = standard
deviation
r =correlation
coefficient

Free

Free

Free

Free

Fixed

60

8


6

9

9

(21)

60

Generalization =
descriptive hypothesis

The Statistics

Parametric Statistics

D a t a t ype / Le v e l

St a t ist ics t e ch n iqu e s


Nominal

1. Binomial test
2. On sample chi square

Ordinal

1. Run test

Interval / ratio

1. On sample
p t-test

† Parametric statistics is used for
interval or ratio data type
† Tested by t-test (unknown population
std dev.)
std.

de ) or
o z-test
test (kno
(known
n pop
population
lation
std. dev.)

t=

X −μ

o

s
n

© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!


1

07/05/2011

Two Tailed Vs One Tail

7 Steps of Manually Test

Tw o t a il

On e t a il

† Ho : Shop keeper can
standing = 8 hours
every day
† Ha : Shop keeper
can’t standing ≠ 8
hours every day
† Ho : μ = 8 hours

† Ha : μ ≠ 8 hours

Uppe r t a il
† Ho : μ ≥
† Ha : μ <
Low e r t a il
† Ho : μ ≤
† Ha : μ >

1.
2.
3.
4
4.
5.
6.

Count data mean
Count standard deviation
Count t value

Sea h t table value
Search
al e
Draw distribution curve
Putting counted t value and t table
value on the curve
7. Make decision about hypothesis test

8 hours
8 hours
8 hours
8 hours

Statistic Parametric: Binomial
Test

Statistic Parametric: Chi Square

† Nominal data
† Two class groups

(man-women; poorrich)
† Small sample size
(25)
Ho: Men and women
have same chance to
be elected as
president
Ha: Men and women
haven’t got same
chance to be elected
as president

† Ho: P1 = P2 = 0.5
† Ha: P1 ≠ P2 ≠ 0.5

P

(x)

⎛N⎞

= ⎜⎜ ⎟⎟
⎝x⎠

x

p .q

N −x

⎛N⎞
N!
⎜⎜ x ⎟⎟ = x!( N − x)!
⎝ ⎠

Statistic Parametric: Run Test
r−μ
† Ordinal data
r
† Sequence test
z=


† Tested by randomize
test
Ho: In an election
queue is random
(independent/not
manipulated)
Ha: In an election
queue isn’t random
(dependent/manipul
ated)

σ

r

=

r

2n n (2n n − n − n )
(n1+ n2) (n + n − 1)
1

2

1
2

2

1

1

2

(f −f )
χ =∑ o h
f

2

2

k

i =1

h

Kit a m enilai diri kit a sendiri
dengan apa yang kit a rasa m am pu
lakukan,
sedangkan orang lain m enilai kit a
dengan apa yang t elah kit a lakukan



μ r = ⎜⎜ 2n+1 n2 + 1⎟⎟ − 0.5
⎝ n1 n2 ⎠

σ

† Ho: People have
same chance to
choose four car color
† Ha: People haven’t
got same chance to
choose four car color

2

= = HENRY WADSWORTH LOGNFELLOW,

KAVANAGH, 1849 = =

© Mahendra Adhi Nugroho, M.Sc, Accounting Program Study of Yogyakarta State University
For internal use only!

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