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

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

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

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

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.

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

(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.

(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.

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

(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.

n 72

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

Population correction.

n2 = n1 + 10% n2 = sampel akhir.

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

Soal (1) :

Alpha = 5% = 5%

p = 0.30 = 0.40 = 0.50

L = 10% = 10 %

Key : n = 81 n = 92 n = 96

N = 666

Soal (2) :

Alpha = 5%

p = 0.63

L = 10%

Key : n = 89

N = 666

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.

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 ?

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.

(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.

Rumus Standard deviation gabungan :

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

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

n1 + n2 - 2

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

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

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

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

3. Rumus Sample Size utk Uji Korelasi.

(1 – r 2)(Zα+Zβ) 2

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

r 2

n = Besar sampel minimal.

r = Koefisien Korelasi.

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

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.

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

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

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