Uji hipotesa dan interval kepercayaan.pdf

8/10/2019 Uji hipotesa dan interval kepercayaan.pdf

1/41

Dr. Pudji Lestari,dr,Mkes

IKM-KP Kedokteran Unair

Uji hipotesa dan interval kepercayaan


2/41

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


3/41

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


4/41

Hypothesis Testing

Test Result

True State

H0True H0False

H0True Correct

Decision

Type I Error

H0False Type II Error Correct

Decision

)()( ErrorIITypePErrorITypeP

Tujuan : , keciilll


5/41

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


6/41

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)


7/41

One tail or two tail


8/41

Pilih uji statistik yang sesuai- Tergantung tujuan panelitian

- Tergantung jenis datanya

- Tergantung asumsi distribusinya (normal/menceng)

- Ukuran sampel/besar sampelnya (n>30 at n


9/41


10/41


11/41

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


12/41

Bandingkan p dengan

P adalah probabilitas diterimanya Ho

adalah level kesalahan yang toleransi

Bila p> maka Ho di terimaBila p < maka H1 di terima


13/41

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


14/41

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


15/41

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


16/41

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


17/41

Power of a Test

Distribution (H0

) Distribution (HA

)


18/41

ESTIM TION

Pudji lestari dr, MKes

Public Health Dept School of Medicine AirlanggaUniversity


19/41

As taking sampleis takingsome risk,

so statistics is deal with

calculating the risk, then estimation is the

way to express it

x


20/41

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


21/41

x

once the sample size is 30 or more

sampling distribution is normal

distribution (Central Limit Theory)

n/x


22/41


23/41


24/41


25/41

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.


26/41

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.


27/41

General Confidence Interval

Calculation

Point Estimate Critical

Value) Standard Error)


28/41

Confidence Interval Estimate

for (known) is given by

n

x z


29/41

Confidence Interval Estimate

for (unknown)

n

s)(x2

1 dkt


30/41

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


31/41

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.


32/41

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


33/41

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.


34/41

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.


35/41

Proportion Estimation


36/41

Proportion Estimation

)(p2

pSEz


37/41

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


38/41

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


39/41

Estimating Sample Size

The amount ofsampling erroryou arewilling to accept and the

level ofconfidence desired, determines the size of your sample.


40/41

Confident interval and p value


41/41

Clinical important and

statistically important

Uji hipotesa dan interval kepercayaan.pdf

Documents

Transcript of Uji hipotesa dan interval kepercayaan.pdf