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
Population
parameter
μ = mean
σ = standard
deviation
ρ = proportion
Degree of freedom Concept
Reduction
Statistic
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
Data type/Level
Statistics techniques
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
Two tail
One tail
† 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
Upper tail
† Ho : μ ≥
† Ha : μ <
Lower tail
† 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 : people have same
chance to choose
gasoline car or diesel
car, that is 50%
Ho : people haven’t got
same chance to
choose gasoline car or
diesel car, that is 50%
† Nominal data
† Two or more
categories
† Big 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
Kita menilai diri kita sendiri
dengan apa yang kita rasa mampu
lakukan,
sedangkan orang lain menilai kita
dengan apa yang telah kita 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