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!
2
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!
2