uji hipotesa dan interval kepercayaan.pdf
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Dr. Pudji Lestari,dr,Mkes
IKM-KP Kedokteran Unair
Uji hipotesa dan interval kepercayaan
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Apa ?? Hypo = lemah
Thesis : dugaan
Uji Hypotesis : menguji dugaan yg lemah
An educated guess A claim or statement about a property of
a population
Tujuan : menganalisa suatu sample
dalam upaya membedakan karakteristikpopulasi yang mungkin muncul dan ygmungkintidak muncul
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Elements of a hypothesis test
Null hypothesisHo Statement regarding the value(s) ofunknown parameter(s). Typically will imply no association
between explanatory and response variables in our applications
(will always contain an equality)
Alternative hypothesisH1Statement contradictory to thenull hypothesis (will always contain an inequality)
Test statistic - Quantity based on sample data and null
hypothesis used to test between null and alternative hypotheses
Rejection region -Values of the test statistic for which wereject the null in favor of the alternative hypothesis
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Hypothesis Testing
Test Result
True State
H0True H0False
H0True Correct
Decision
Type I Error
H0False Type II Error Correct
Decision
)()( ErrorIITypePErrorITypeP
Tujuan : , keciilll
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Power of a Test
Power - Probability a test rejects H0 (depends on m1- m2) H0True: Power = P(Type I error) =
H0False: Power = 1-P(Type II error) = 1-
As sample sizes increase, power increases
As population variances decrease, power increases
As the true mean difference increases, power increases
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Prosedur Uji hipotesa
Tentukan Tujuan hipotesa:
membandingkan (komparasi), melihat adakah hubungan
(korelasi)--(dalam satu riset bisa lebih dari satu tujuan)
Formulasikan hipotesis
Ho = netral
H1= alternative ,yang ingin dibuktikan
searah (tendensius), dua arah (nontendensius)
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One tail or two tail
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Pilih uji statistik yang sesuai- Tergantung tujuan panelitian
- Tergantung jenis datanya
- Tergantung asumsi distribusinya (normal/menceng)
- Ukuran sampel/besar sampelnya (n>30 at n
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Pasang nya
= tingkat kemaknaan = tingkat kesalahan yang ditoleransi
=kemungkinan Ho ditolak padahal Ho benar
Tergantung peneliti Besar bila penelitian sosial atau lapangan
kecil bila penelitian klinik
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Bandingkan p dengan
P adalah probabilitas diterimanya Ho
adalah level kesalahan yang toleransi
Bila p> maka Ho di terimaBila p < maka H1 di terima
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Contoh - Efficacy Test for New drug
Pabrik Obat ingin membandingkan obat hipertensi baru
dengan obat standar Untuk mendapatkan izin edar, harus ada fakta yang
cukup untuk menunjukkan bahwa obat baru lebih baik.
Dilakukan uji klinik , sekelompok penderita dengan obatbaru, dan sekelompok yang lain dengan obat standar
Untuk melihat respon terhadap obat di lakukan
pengukuran oleh tenaga terlatih dan instrumen
terstandar. Parameter of interest: mNew- mStd
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Contoh - Efficacy Test for New drug
Type I errorH nol ditolak padahal Hnol benarmenyimpulkan bahwa obat baru lebih baik padahal sama
dengan obat standar
Traditionally = P(Type I error) = 0.05
Type II errorH1 ditolak padahal H1 benar. Gagalmenunjukkan bahwa obat baru efektif seperti seharusnya.
Traditionally a clinically important difference (D)is assigned and sample
sizes chosen so that:
= P(Type II error | m1-m2= D) .20
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Elements of a Hypothesis Test
Test Statisticperbedaan antara Sample means, diskalakanterhadap jumlah SD (standard errors) dari 0 Population means:
2
2
2
1
2
1
21
:..
n
s
n
s
yy
zST obs
Rejection Region -Set of values of the test statistic that are consistent
with HA, such that the probability it falls in this region when H0is true is (we will always set =0.05)
645.105.0:.. zzzRR obs
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P-value (aka Observed Significance Level)
P-value - Measure of the strength of evidence the sample data
provides against the null hypothesis:
P(Evidence This strong or stronger against H0| H0is true)
)(: obszZPpvalP
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Power of a Test
Distribution (H0
) Distribution (HA
)
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ESTIM TION
Pudji lestari dr, MKes
Public Health Dept School of Medicine AirlanggaUniversity
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As taking sampleis takingsome risk,
so statistics is deal with
calculating the risk, then estimation is the
way to express it
x
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Some possible samples = some sample means and samplestandard deviations
These sample means the sampling distribution of the
mean (Normal)
mean of the sampling distribution =
the standard deviation of the sampling distribution =
Sampling Review
x
x
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x
once the sample size is 30 or more
sampling distribution is normal
distribution (Central Limit Theory)
n/x
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Point Estimates
a singlenumber from sample used to estimate thecorresponding populationparameter(e.g., the sample
mean).
a newspaper state from sample that 65% of all adults inSurabaya think that the Hospital should be cleaner.
The percentage of the sample who agree that e Hospital
should be cleaner is the point estimate for the true
population percentage who agree.
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Confidence Intervals
an intervalin which we are confident the population
parameter will lie.
rather than give a particular value as the estimate for a
population parameter
find the limits of the interval.
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General Confidence Interval
Calculation
Point Estimate Critical
Value) Standard Error)
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Confidence Interval Estimate
for (known) is given by
n
x z
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Confidence Interval Estimate
for (unknown)
n
s)(x2
1 dkt
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Example:
As a consultant I have been employed to estimate the averageamount of comp time accumulated per week for nurse in thehospital.
I randomly sample 18 nurse and measure the amount of extratime they work during a specific week and obtain the followingresults (in hours). Assume a 90% confidence interval.
Hospital DATA
6 21 17 20 7 0 8 16
293 8 12 11 9 21 25 15 16
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Solution:
To construct a 90% confidence interval to estimate the averageamount of extra timeper week worked by anurse in the hospital ,Iassumethat comp time is normally distributedin thepopulation.
The sample size is 18, so df = 17.
A 90% level of confidence results in an / 2 = .05area in each tail.
The table t-value is t .05,17= 1.740.
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With a sample mean of 13.56 hours, and a sample standard
deviation of 7.8 hours, the confidence interval is computed:
X-bar +/- t/2, n-1S / n
=13.56 +/- 1.740 ( 7.8 / 18) = 13.56 +/- 3.20= 10.36 16.76
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Interpretation
The point estimate for this problem is 13.56 hours,with an error of +/- 3.20 hours.
I am 90% confident that the average amount of comp
time accumulated by a Nurse per week in this
hospital is between 10.36 and 16.76 hours.
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Recommendations
From these figures, the hospital could attempt tobuild a reward system for such extra work or
evaluate the regular 40-hour week to determine
how to use the normal work hours more effectively
and thus reduce comp time.
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Proportion Estimation
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Proportion Estimation
)(p2
pSEz
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Variance Estimation
dkdk
SS
/
2
22
/1
2
2
2
1
2
1
Where 2 /dk is Chi Square distribution per degree of
freedom. Tabel A-6b
dk = n 1 which n is sample size
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Example
Ten students have monthly money variance 300 ribu rupiah ,as the confident interval 90% , estimate variance of all
students !
160 < 2< 813
12,6 < < 28,5
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Estimating Sample Size
The amount ofsampling erroryou arewilling to accept and the
level ofconfidence desired, determines the size of your sample.
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Confident interval and p value
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Clinical important and
statistically important