 # 1 Pertemuan 11 Matakuliah: I0014 / Biostatistika Tahun: 2005 Versi: V1 / R1 Pengujian Hipotesis (I)

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1 Pertemuan 11 Matakuliah: I0014 / Biostatistika Tahun: 2005 Versi: V1 / R1 Pengujian Hipotesis (I)

2 Learning Outcomes Pada akhir pertemuan ini, diharapkan mahasiswa akan mampu : Mahasiswa dapat menjelaskan konsep pengujian hipotesis (C2) Mahasiswa dapat menguji hipotesis untuk nilai tengah (C3)

3 Outline Materi Pendugaan Nilai tengah Pendugaan beda dua nilai tengah

4 A null hypothesis, denoted by H 0, is an assertion about one or more population parameters. This is the assertion we hold to be true until we have sufficient statistical evidence to conclude otherwise. – H 0 :  =100 The alternative hypothesis, denoted by H 1, is the assertion of all situations not covered by the null hypothesis. – H 1 :  100 H 0 and H 1 are: – Mutually exclusive –Only one can be true. –Exhaustive –Together they cover all possibilities, so one or the other must be true. H 0 and H 1 are: – Mutually exclusive –Only one can be true. –Exhaustive –Together they cover all possibilities, so one or the other must be true. Pengujian Hipotesis >

5 A contingency table illustrates the possible outcomes of a statistical hypothesis test. Logika Pengujian Hipotesis >

6 A decision may be incorrect in two ways: – Type I Error: Reject a true H 0 The Probability of a Type I error is denoted by .  is called the level of significance of the test – Type II Error: Accept a false H 0 The Probability of a Type II error is denoted by . 1 -  is called the power of the test.  and  are conditional probabilities: Kesalahan dalam Uji Hipotesis >

7 Critical Points of z Pengujian Mean Populasi (n besar) >

8 Small-sample test statistic for thepopulation mean, : t= x- s n When the populationis normally distributed and the null hypothesis is true, the teststatistichas a distribution with degrees of freedom 0   t n-1 When the population is normal, the population standard deviation, , is unknown and the sample size is small, the hypothesis test is based on the t distribution, with (n-1) degrees of freedom, rather than the standard normal distribution. Pengujian Mean Populasi (n kecil) >

9 Uji mean berpasangan (pair t test) >

10 When paired data cannot be obtained, use independent random samples drawn at different times or under different circumstances. –Large sample test if: Both n 1  30 and n 2  30 (Central Limit Theorem), or Both populations are normal and  1 and  2 are both known –Small sample test if: Both populations are normal and  1 and  2 are unknown Uji Mean Dua Populasi Independen >

11 I: Difference between two population means is 0 H 0 :  1 -  2 = 0 H 1 :  1 -  2  0 II: Difference between two population means is less than 0 H 0 :  1 -  2  0 H 1 :  1 -  2  0 III: Difference between two population means is less than D H 0 :  1 -  2  D H 1 :  1 -  2  D Situasi Pengujian Dua Mean Populasi >

12 Large-sample test statistic for the difference between two population means: The term (  1 -  2 ) 0 is the difference between  1 an  2 under the null hypothesis. Is is equal to zero in situations I and II, and it is equal to the prespecified value D in situation III. The term in the denominator is the standard deviation of the difference between the two sample means (it relies on the assumption that the two samples are independent). Large-sample test statistic for the difference between two population means: The term (  1 -  2 ) 0 is the difference between  1 an  2 under the null hypothesis. Is is equal to zero in situations I and II, and it is equal to the prespecified value D in situation III. The term in the denominator is the standard deviation of the difference between the two sample means (it relies on the assumption that the two samples are independent). Statistik Uji Dua Mean Populasi >

13 When sample sizes are small (n 1 < 30 or n 2 < 30 or both), and both populations are normally distributed, the test statistic has approximately a t distribution with degrees of freedom given by (round downward to the nearest integer if necessary): Uji Dua Mean Populasi dengan Ukuran Contoh Kecil >

14 Menggunakan Ragam gabungan (Pooled Variance) >

15 > Sampai saat ini Anda telah mempelajari pengujian hipotesis nilai tengah, baik untuk satu populasi maupun dua populasi Untuk dapat lebih memahami penggunaan pengujian hipotesis tersebut, cobalah Anda pelajari materi penunjang, dan mengerjakan latihan

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