xd_sample size usakti

26
Sample Penelitian Sumedi Sudarsono 2012 Sample is a portion of the population A sample must representative for the population. Sampling Error 5% = 0.05 (1). Random (2). Equal probability

Upload: ayu-wulan-anggreni

Post on 08-Nov-2014

24 views

Category:

Documents


3 download

DESCRIPTION

ikm 2

TRANSCRIPT

Page 1: Xd_sample Size Usakti

Sample Penelitian Sumedi Sudarsono 2012

Sample is a portion of the population

A sample must representative for the population.

Sampling Error 5% = 0.05

(1). Random (2). Equal probability

Page 2: Xd_sample Size Usakti

The idea of sampling is to study a part of the population in order to gain information about the whole population.

Advantages of a sample :

1. Reduce finance, personnel, material, lower

cost

2. Results more quickly, shorter time

3. Better accuracy

4. More comprehensive data

Page 3: Xd_sample Size Usakti

Sample size depends on :

1. Study design

2. Estimated magnitude of the parameter being studied ( = p )

3. Variability of the parameter being studied (s)

4. Level or Error ( = α )

5. Level of precision ( L )

6. Data analysis plan

7. Practical consideration

Page 4: Xd_sample Size Usakti

1. Longitudinal study design requires larger sample than cross-sectional study

Cluster sampling design requires larger sample than simple random sampling

2. p = prevalence being studied, q = 1 – p

when p = 0.5 then maximun sample size is reached

3. The rarer the variable being studied, the larger the sample size

Page 5: Xd_sample Size Usakti

4. The more heterogeneous the variable in the population, the larger the sample size.

5.The higher the level of precision desired, the larger the sample size.

6. Multivariate data analysis required larger sample size than univariate analysis.

7. Practical consideration : money, man power,

time allocation.

Page 6: Xd_sample Size Usakti

Besar sampel tergantung desain penelitian

1. Desain prevalensi (survei), cross sectional

a). Data kategori

b). Data numerik

2. Desain membandingkan dua mean

a). t-independent

b). t-berpasangan

3. Desain korelasi

4. Desain kohort atau eksperimen

5. Desain kasus-kontrol

Page 7: Xd_sample Size Usakti

(1). Besar Sampel Studi Prevalensi.

1. Tergt pd tingkat kesalahan α Zα .

utk α=5% lihat Tabel, maka Zα = 1.960

2. Proporsi variabel yg diteliti, didpt dari

kepustakaan, dinyatakan dg ‘p’.

Contoh : variabel cacingan pada anak SD

diket. p = 0.75 maka q = 0.25

3. Presisi / ketepatan, biasa L = 5% atau 10%

4. Hitung Koreksi Populasi.

5. Hitung besar sampel minimal.

Page 8: Xd_sample Size Usakti

(Zα) 2 p q Utk DATA KATEGORI

n = ---------------- ( proporsi )

L 2 n = Besar sampel awal.

n

n1 = --------------- n1 = Population correction. 1 + n/N

N = Besar Populasi.

n2 = n1 + 10% n2 = sampel akhir.

Page 9: Xd_sample Size Usakti

Tabel Distribusi Normal

α Zα------------------------- Semakin kecil α0.05 1.960 maka semakin besar0.025 2.248* nilai Zα nya. 0.020 2.3260.01 2.576 semakin besar0.005 2.813* ukuran sampelnya.0.001 3.291-------------------------- Rujuk Table A3

Page 10: Xd_sample Size Usakti

(Zα) 2 p q p = 0,75 q = 0.25

n = ---------------- α = 0.05 Zα = 1.960

L 2 L = 0.10

(1.96) 2 (0.75) (0.25)

n = ----------------------------- = 72

(0.10) 2

Bila diketahui POPULASI = 300.

Page 11: Xd_sample Size Usakti

n 72

n1 = --------------- = ------------------ = 58 1 + n/N 1 + 72/300

Population correction.

n2 = n1 + 10% n2 = sampel akhir.

n2 = 58 + (10%)(58) = 64

Page 12: Xd_sample Size Usakti

Soal (1) :

Alpha = 5% = 5%

p = 0.30 = 0.40 = 0.50

L = 10% = 10 %

Key : n = 81 n = 92 n = 96

N = 666

Page 13: Xd_sample Size Usakti

Soal (2) :

Alpha = 5%

p = 0.63

L = 10%

Key : n = 89

N = 666

Page 14: Xd_sample Size Usakti

Rumus Sample Size utk Survei / prevalensiData Numerik. Contoh : Kadar HB bumil.

( gram/dL ).

Zα (s)

n = { ----------- } 2

d

α = Tingkat kemaknaan / kesalahan type I.

s = Simpang baku = Standard deviation.

d = Presisi.

Page 15: Xd_sample Size Usakti

Contoh :

Studi survei tentang kadar Hb bumil di Cemp

Putih Barat, waktu ….. th …..

Dari jurnal dikertahui simpang baku = 0.45 g/dL

Presisi = 10 % dan α = 5 %

Berapa besar sampel yg diperlukan ?

Page 16: Xd_sample Size Usakti

Zα (s) α = 0.05 Zα = 1.960

n = { ----------- } 2 s = 0.45 d = 0.10 d

(1.96) (0.45)

n = { ---------------- } 2 = 78

0.10

Besar sampel yg diperlukan =

78 + 10% = 86 bumil.

Page 17: Xd_sample Size Usakti

(2). Rumus Sample Size utk

Uji t-independent

(Zα + Zβ) 2 s 2

n = 2 ---------------------------- (mean1 – mean2) 2

n = besar sampel minimal.α = kesalahan tipe I.β = kesalahan tipe II.s = standard deviation gabungan.

Page 18: Xd_sample Size Usakti

Rumus Standard deviation gabungan :

(s1) 2 (n1-1) + (s2) 2 (n2-1)

s g = √ { -------------------------------------- }

n1 + n2 - 2

Page 19: Xd_sample Size Usakti

Tabel Beta ( 1 – β ) = Power penelitian.

β Zβ

----------------------------- Semakin besar Power

20% 0.842 semakin besar Zβ 10% 1.282 semakin besar

5% 1.645 sampelnya.

1% 2.326

0.05% 2.576

-----------------------------

Page 20: Xd_sample Size Usakti

s = 1.5 mean1 – mean2 = 1 g/dL

alpha = 5% Power = 80% Sample size = ?

(Zα + Zβ) 2 s 2

n = 2 ----------------------------

(mean1 – mean2) 2

(1.96 + 0.842) 2 (1.5) 2

n = 2 ---------------------------------- = 35

(1 ) 2 for each group

Page 21: Xd_sample Size Usakti

T-test pairs

(Zα + Zβ) 2 s 2

n = ------------------------

(mean dif) 2

s =1.2 g/dL mean dif = 0.5 g/dL α = 5%

Power = 80%

(1.96 + 0.842) 2 (1.2)2

n = -------------------------------- = 45

( 0.5) 2

Page 22: Xd_sample Size Usakti

3. Rumus Sample Size utk Uji Korelasi.

(1 – r 2)(Zα+Zβ) 2

n = ------------------------- + 2

r 2

n = Besar sampel minimal.

r = Koefisien Korelasi.

Page 23: Xd_sample Size Usakti

4. Sample Size Studi Kohort / Experiment.

{Zα√(2pq) + Zβ√(p1q1+p2q2)}2

n = -------------------------------------------

(p1-p2) 2

p1 = Proporsi sembuh kelompok standard.

p2 = Proporsi sembuh kelompok perlakuan.

p1 + p2

p = ------------------

2

Page 24: Xd_sample Size Usakti

5. Rumus Sample Size Studi Case-control.

1. Proporsi kontrol = p2, misal = 0.10

2. Perkiraan besar OR, misal = 3.0

3. Besar α

4. Besar presisi = e

p2 (OR)

maka p1 = ----------------------

(1-p2) + p2(OR)

p1 = Proporsi kasus.

Page 25: Xd_sample Size Usakti

p2 (OR) 0.10 (3)

p1 = ----------------------- = ------------------------

(1-p2) + p2 (OR) (1-0.10) + 0.10 (3)

p1 = 0.25

(Zα) 2 [(p1/q1) + (p2/q2)] 2

n = --------------------------------------

[ ln (1 – e) ] 2

Page 26: Xd_sample Size Usakti

Perbedaan antara Log dg Ln.

1. Log 2 = 0.3010 Ln 2 = 0.6931

2. Log 3 = 0.4771 Ln 3 = 1.0986

3. Log 4 = 0.6021 Ln 4 = 1.3863

==========o0o==========Finish