Pengujian Hipotesis (I) Pertemuan 11 Matakuliah : I0014 / Biostatistika Tahun : 2008 Pengujian Hipotesis (I) Pertemuan 11

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) Bina Nusantara

Outline Materi Pendugaan Nilai tengah Pendugaan beda dua nilai tengah Bina Nusantara

Pengujian Hipotesis A null hypothesis, denoted by H0, 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. H0: =100 The alternative hypothesis, denoted by H1, is the assertion of all situations not covered by the null hypothesis. H1: 100 H0 and H1 are: Mutually exclusive Only one can be true. Exhaustive Together they cover all possibilities, so one or the other must be true. Bina Nusantara

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

Kesalahan dalam Uji Hipotesis A decision may be incorrect in two ways: Type I Error: Reject a true H0 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 H0 The Probability of a Type II error is denoted by . 1 -  is called the power of the test.  and  are conditional probabilities: Bina Nusantara

Pengujian Mean Populasi (n besar) Critical Points of z Bina Nusantara

Pengujian Mean Populasi (n kecil) 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. Small - sample tes t statisti c for the population mean, : t = x s n When the p opulation is normall y distribu ted and th e null hypothesis is true, the test statistic has a distribut ion with degrees o f freedom m 1 Bina Nusantara

Uji mean berpasangan (pair t test) Bina Nusantara

Uji Mean Dua Populasi Independen When paired data cannot be obtained, use independent random samples drawn at different times or under different circumstances. Large sample test if: Both n1  30 and n2  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 Bina Nusantara

Situasi Pengujian Dua Mean Populasi I: Difference between two population means is 0 H0: 1 -2 = 0 H1: 1 -2  0 II: Difference between two population means is less than 0 H0: 1 -2  0 H1: 1 -2  0 III: Difference between two population means is less than D H0: 1 -2  D H1: 1 -2  D Bina Nusantara

Statistik Uji Dua Mean Populasi 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). Bina Nusantara

Uji Dua Mean Populasi dengan Ukuran Contoh Kecil When sample sizes are small (n1< 30 or n2< 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): Bina Nusantara

Menggunakan Ragam gabungan (Pooled Variance) Bina Nusantara

Penutup 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 Bina Nusantara