Analisis Ragam Gabungan Dengan Ragam Tidak Homogen (Studi Kasus Percobaan Multilokasi Budidaya Jahe Di Jawa Barat)

Abstract

Combined analysis of variance has several rigid assumptions. One of them is homogeneity of variance which in many cases is failed to be fulfilled. So there should be a statistical approach to handle this problem. Classical liniear model of data from an experiment assumes the homogeneity of variance. If it is violated then usually the data will be transformed to achieve linearity of the model. But one problem in using transformed data is difficulty in interpreting it. Other approach used for handling this problem is organizing the data into groups based on the similarity of variance. One procedure that uses this kind of approach is Mixed Procedure. The objectives of this research were to distinguish the interaction between the little white ginger expected genotype and its cultivation location and to study the technique of handling heterogeneity of variance in Combined Analysis of Variance. The data used in this research was experiments data of little white ginger produced by researcher of Indon Spices and Medical Crops Research Institute (ISMECRI) Bogor. The experiment was conducted in five location: Sukamulya, Wado, Malangbong, Garut, and Majalengka. The single experiment was accomplished by cultivating seven little white ginger expected genotype. The environmental design was Randomize Complete Block Design with three repetitions and the response was the amount of ginger young plants. Three analysis’ of variance with different covariance matrix conclude significant interaction between location and genotype. Log-likelihood ratio of each model covariance matrix was used to select the best model wich turns out to be the model with revision of location groups. The treatment significance test with the assumption that the variance between locations is not homogeny result greater p-value compared to the treatment significance test with revised estimated variance. This means that the treatment significance test with the assumption that the variance between locations is not homogeny has lesser accuracy level than the treatment significance test with revised estimated variance on the same level of significance. Likewise, the treatment significant test with transformed data has lesser accuracy level than the treatment significance test with revised estimated variance. The appropriate organization of the data into groups on the similarity of variance (proper selection of covariance matrix) can increase accuracy of treatment significance test for cases when the variance is not homogeny.