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ANALISIS UNIVARIAT. Statistik Univariat. Menguji Keertian Statistik Menguji Hipotesis satu pembolehubah per satu (tiap kali). Hipotesis. Proposisi ( cadangan) yang belum terbukti Andaian bagi menerangkan sesuatu fakta atau Andaian mengenai keadaan dunia

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statistik univariat
Statistik Univariat
  • Menguji Keertian Statistik
  • Menguji Hipotesis satu pembolehubah per satu (tiap kali).
hipotesis
Hipotesis
  • Proposisi ( cadangan) yang belum terbukti
  • Andaian bagi menerangkan sesuatu fakta atau
  • Andaian mengenai keadaan dunia
    • (Dalam ertikata yang lain hipotesis adalah jangkaan)
hipotesis1
Hipotesis
  • Proposisi atau andaian belum terbukti bagi menerangkan sesuati fakta atau fenomena.
    • Hipootesis Nol
    • Hipotesis Alternatif
      • Hoptesis nol adalah hipotesis yang status quo atau kedudukan semasa, tidak berubah.
      • Hipotesis alternatif adalah hipotesis yang bertentangan.
      • Contoh: Aras jualan mingguan tidak berbeza dengan purata jualan mingguan dengan penawaran diskaun harga 20 sen.
      • Jumlah pembelian menggunakan kad keredit tidak berbeza dengan bayaran secara tunai.
proses menguji hipotesis
Proses Menguji Hipotesis
  • Menentukan apakah hipotesis yang hendak diuji secara statistik.
  • Menggambarkan apakahtaburan persampelan mean jika pernyataan hipotesis adalah benar menerangkan tetang keadaan populasi.
  • Mendapatkan sampel sebenar dan menentukan mean sampel tersebut(atau statistik yang sesuai)
slide6
Kita memang menjangkakan bahawa memang wujud perbezaan kecil diantara sampel dan populasi. Namun begitu kita pelu menguji sama ada perbezaan ini kecil atau sangat ketara dengan mean dari taburan persampelan mean. Jika wujud perbezaan yang ketara, kita tidak boleh membuat kesimpulan begitu sahaja sama ada memerima atau menolak hipotesis nol. Kita harus merujuk kepada peraturan membuat keputusan yang terpiawai. Ini dipanggil dalam bidang statistik sebagai aras keertian.
slide7
3. Keputusan menerima atau menolak hipotesi nol akan dibuat jika perbezaan tersebut diperingkat keertian kurang daripada 0.05 ( <0.05) atau diluar diluar kawasan penerimaan.
aras keertian
Aras Keertian
  • Kebangkalian kritikal sama ada memilih hipotesis nol atau hipotesis alternatif
aras keertian1
Aras Keertian
  • Kebangkalian kritikal
  • Aras keyakinan
  • Alpha
  • Aras Kebarangkalian yang dipilih biasanya .05 atau .01
  • Terlalu rendah untuk menyokong hipotesis nol
slide10

Example: A study on consumer perception of service quality- friendly or not friendly. Measurement 5 point-point scale, assumed to be an interval scale. 5- very friendly and 1- very unfriendly. A sample of 225 respondents were taken. The mean score from the sample equaled 3.75 and sample standard deviation S=1.5

The null hypothesis that the mean is equal to 3.0:

a sampling distribution1
A Sampling Distribution

a=.025

a=.025

m=3.0

a sampling distribution2
A Sampling Distribution

UPPER

LIMIT

LOWER

LIMIT

m=3.0

standardized sampling distribution
Standardized Sampling Distribution

Z=1.96

UPPER

LIMIT

LOWER

LIMIT

-1

1

m=0

Z

slide16

Critical values ofm

Critical value - upper limit

slide18

Critical values ofm

Critical value - lower limit

region of rejection
Region of Rejection

LOWER

LIMIT

m=3.0

UPPER

LIMIT

hypothesis test m 3 0
Hypothesis Test m =3.0

2.804

3.78

m=3.0

3.196

type i and type ii errors
Type I and Type II Errors

Accept null

Reject null

Null is true

Correct-

no error

Type I

error

Null is false

Type II

error

Correct-

no error

slide23

Type I and Type II Errors

in Hypothesis Testing

State of Null Hypothesis Decision

in the Population Accept Ho Reject Ho

Ho is true Correct--no error Type I error

Ho is false Type II error Correct--no error

choosing the appropriate statistical technique
Choosing the Appropriate Statistical Technique
  • Type of question to be answered
  • Number of variables
    • Univariate
    • Bivariate
    • Multivariate
  • Scale of measurement
slide28

NONPARAMETRIC

STATISTICS

PARAMETRIC

STATISTICS

t distribution
t-Distribution
  • Symmetrical, bell-shaped distribution
  • Mean of zero and a unit standard deviation
  • Shape influenced by degrees of freedom
degrees of freedom
Degrees of Freedom
  • Abbreviated d.f.
  • Number of observations
  • Number of constraints
slide32

Confidence Interval Estimate Using the t-distribution

= population mean

= sample mean

= critical value of t at a specified confidence

level

= standard error of the mean

= sample standard deviation

= sample size

univariate hypothesis test utilizing the t distribution
Univariate Hypothesis Test Utilizing the t-Distribution

Suppose that a production manager believes the average number of defective assemblies each day to be 20. The factory records the number of defective assemblies for each of the 25 days it was opened in a given month. The mean was calculated to be 22, and the standard deviation, ,to be 5.

univariate hypothesis test utilizing the t distribution1
Univariate Hypothesis Test Utilizing the t-Distribution

The researcher desired a 95 percent confidence, and the significance level becomes .05.The researcher must then find the upper and lower limits of the confidence interval to determine the region of rejection. Thus, the value of t is needed. For 24 degrees of freedom (n-1, 25-1), the t-value is 2.064.

testing a hypothesis about a distribution
Testing a Hypothesis about a Distribution
  • Chi-Square test
  • Test for significance in the analysis of frequency distributions
  • Compare observed frequencies with expected frequencies
  • “Goodness of Fit”
chi square test1
Chi-Square Test

x² = chi-square statistics

Oi = observed frequency in the ith cell

Ei = expected frequency on the ith cell

chi square test estimation for expected number for each cell1
Chi-Square Test Estimation for Expected Number for Each Cell

Ri = total observed frequency in the ith row

Cj = total observed frequency in the jth column

n = sample size

hypothesis test of a proportion
Hypothesis Test of a Proportion

p is the population proportion

p is the sample proportion

p is estimated with p

hypothesis test of a proportion another example

=

n

1

,

200

=

p

.

20

pq

=

S

p

n

(.

2

)(.

8

)

=

S

p

1200

.

16

=

S

p

1200

=

S

.

000133

p

=

S

.

0115

p

Hypothesis Test of a Proportion: Another Example
hypothesis test of a proportion another example1

=

n

1

,

200

=

p

.

20

pq

=

S

p

n

(.

2

)(.

8

)

=

S

p

1200

.

16

=

S

p

1200

=

S

.

000133

p

=

S

.

0115

p

Hypothesis Test of a Proportion: Another Example
hypothesis test of a proportion another example2

The

Z

value

exceeds

1.96,

so

the

null

hypothesis

should

be

rejected

at

the

.05

level.

it

is

significant

t

beyond

the

.001

Hypothesis Test of a Proportion: Another Example

-

p

p

=

Z

S

p

-

.

20

.

15

=

Z

.

0115

.

05

=

Z

.

0115

=

Z

4

.

348

Indeed