1. Pertemuan 17 Analisis Varians Klasifikasi Satu Arah
Matakuliah : I Statistika
Tahun : 2005
Versi : Revisi
Pertemuan 17 Analisis Varians Klasifikasi Satu Arah

2. Learning Outcomes
Pada akhir pertemuan ini, diharapkan mahasiswa
akan mampu :
Mahasiswa akan dapat menyusun simpulan tentang sumber variasi, jumlah kuadrat, derajat bebas dan kuadrat tengah dan uji F.

3. Konsep dasar analisis varians Klasifikasi satu arah ulangan sama
Outline Materi
Konsep dasar analisis varians
Klasifikasi satu arah ulangan sama
Klasifikasi satu arah ulangan tidak sama
Prosedur uji F
Pembandingan perlakuan

4. Analysis of Variance and Experimental Design
An Introduction to Analysis of Variance
Analysis of Variance: Testing for the Equality of
k Population Means
Multiple Comparison Procedures
An Introduction to Experimental Design
Completely Randomized Designs
Randomized Block Design

5. An Introduction to Analysis of Variance
Analysis of Variance (ANOVA) can be used to test for the equality of three or more population means using data obtained from observational or experimental studies.
We want to use the sample results to test the following hypotheses.
H0: 1=2=3= = k
Ha: Not all population means are equal
If H0 is rejected, we cannot conclude that all population means are different.
Rejecting H0 means that at least two population means have different values.

6. Assumptions for Analysis of Variance
For each population, the response variable is normally distributed.
The variance of the response variable, denoted 2, is the same for all of the populations.
The observations must be independent.

7. Analysis of Variance: Testing for the Equality of K Population Means
Between-Samples Estimate of Population Variance
Within-Samples Estimate of Population Variance
Comparing the Variance Estimates: The F Test
The ANOVA Table

8. Between-Samples Estimate of Population Variance
A between-samples estimate of 2 is called the mean square between (MSB).
The numerator of MSB is called the sum of squares between (SSB).
The denominator of MSB represents the degrees of freedom associated with SSB. _ =

9. Within-Samples Estimate of Population Variance
The estimate of 2 based on the variation of the sample observations within each sample is called the mean square within (MSW).
The numerator of MSW is called the sum of squares within (SSW).
The denominator of MSW represents the degrees of freedom associated with SSW.

10. Comparing the Variance Estimates: The F Test
If the null hypothesis is true and the ANOVA assumptions are valid, the sampling distribution of MSB/MSW is an F distribution with MSB d.f. equal to k - 1 and MSW d.f. equal to nT - k.
If the means of the k populations are not equal, the value of MSB/MSW will be inflated because MSB overestimates 2.
Hence, we will reject H0 if the resulting value of MSB/MSW appears to be too large to have been selected at random from the appropriate F distribution.

11. Test for the Equality of k Population Means
Hypotheses
H0: 1=2=3= = k
Ha: Not all population means are equal
Test Statistic
F = MSB/MSW
Rejection Rule
Reject H0 if F > F
where the value of F is based on an F distribution with k - 1 numerator degrees of freedom and nT - 1 denominator degrees of freedom.

12. Sampling Distribution of MSTR/MSE
The figure below shows the rejection region associated with a level of significance equal to  where F denotes the critical value.
Do Not Reject H0
Reject H0
MSTR/MSE F
Critical Value

13. The ANOVA Table Source of Sum of Degrees of Mean
Variation Squares Freedom Squares F
Treatment SSTR k MSTR MSTR/MSE
Error SSE nT - k MSE
Total SST nT - 1
SST divided by its degrees of freedom nT - 1 is simply the overall sample variance that would be obtained if we treated the entire nT observations as one data set.

14. Fisher’s LSD Procedure
Hypotheses
H0: i = j
Ha: i j
Test Statistic
Rejection Rule
Reject H0 if t < -ta/2 or t > ta/2
where the value of ta/2 is based on a t distribution
with nT - k degrees of freedom.

15. Fisher’s LSD Procedure Based on the Test Statistic xi - xj_ _
Fisher’s LSD Procedure Based on the Test Statistic xi - xj
Hypotheses
H0: i = j
Ha: i j
Test Statistic xi - xj
Rejection Rule
Reject H0 if |xi - xj| > LSD
where _ _ _ _

16. ANOVA Table for a Completely Randomized Design
Source of Sum of Degrees of Mean
Variation Squares Freedom Squares F
Treatments SSTR k - 1
Error SSE nT - k
Total SST nT - 1

17. Selamat Belajar Semoga Sukses.