A Bivariate Index for Visually Measuring Marginal Inhomogeneity in Square Tables

For square tables, the marginal homogeneity model which has a structure that the row marginal distribution is equal to the column marginal distribution was proposed. Thereafter, various extended models of marginal homogeneity have been proposed, these models can be classified into two types marginal inhomogeneity. On the other hand, various indexes which measure the degree of deviation from marginal homogeneity have been proposed. However these indexes cannot concurrently define degrees of deviation from marginal homogeneity with respect to two types marginal inhomogeneity. This paper proposes a bivariate index that can concurrently define degrees of deviation from those. The proposed bivariate index would also be utility for visually comparing degrees of deviation from marginal homogeneity in several tables using confidence regions.

Extended Marginal Homogeneity Model Based on Complementary Log-Log Transform for Square Tables

For square contingency tables with the same ordinal row and column classifications, McCullagh (1977) gave the marginal cumulative logistic model, which is an extension of the marginal homogeneity (MH) model using the logit transform. The present paper proposes a different extension of the MH model using the complementary log-log transform. In addition, the present paper gives the theorem that the MH model is equivalent to the proposed model and the equality of row and column marginal means holding simultaneously. In data analysis, if the MH model fits the data poorly, the theorem may be useful for seeing the reason for the poor fit. As example, the occupational status data for British father-son pairs are analyzed.

Collapsed Double Symmetry Model and Its Decomposition for Square Contingency Tables

For a square contingency table with ordinal categories, there may be a case that one wants to analyze several collapsed tables obtained by combining some adjacent categories of the original table. This paper proposes some new models which indicate double symmetry, quasi double symmetry and marginal double symmetry for the collapsed square tables. It also gives a decomposition of the double symmetry model for collapsed tables. Two kinds of occupational mobility data are analyzed using new models.

A Measure of Departure from Average Symmetry for Square Contingency Tables with Ordered Categories

For the analysis of square contingency tables, Tomizawa (1994), Tomizawa, Seo, and Yamamoto (1998), and Tomizawa, Miyamoto, and Hatanaka (2001) considered measures to represent the degree of departure from symmetry. However, the maximum value of these measures cannot distinguish two kinds of complete asymmetry (say, complete-upper-asymmetry and complete-lower-asymmetry). The present paper proposes a measure which can distinguish two kinds of complete asymmetry for square tables with ordered categories. Especially the proposed measure is useful for representingthe degree of departure from symmetry when the conditional symmetry model holds. Examples are given.

Decomposition of Symmetry into Ordinal Quasi-Symmetry and Marginal Equimoment for Multi-way Tables

For the analysis of square contingency tables with ordered categories, Agresti (1983) introduced the linear diagonals-parameter symmetry (LDPS) model. Tomizawa (1991) considered an extended LDPS (ELDPS) model, which has one more parameter than the LDPS model. These models are special cases of Caussinus (1965) quasi-symmetry (QS) model. Caussinus showed that the symmetry (S) model is equivalent to the QS model and the marginal homogeneity (MH) model holding simultaneously. For square tables with ordered categories, Agresti (2002, p.430) gave a decomposition for the S model into the ordinal quasi-symmetry and MH models. This paper proposes some decompositions which are different from Caussinus’ and Agresti’s decompositions. It gives (i) two kinds of decomposition theorems of the S model for two-way tables, (ii) extended models corresponding to the LDPS and ELDPS, and the generalized model further for multi-way tables, and (iii) three kinds of decomposition theorems of the S model into their models and marginal equimoment models for multi-way tables. The proposed decompositions may be useful if it is reasonable to assume the underlying multivariate normal distribution.

Pengaruh Program Adiwiyata Terhadap Pengetahuan Perilaku dan Keterampilan Siswa dan Guru dalam Mengelola Lingkungan pada SMK di Kabupaten Pelalawan

Abstrak: The study aimed to determine adiwiyata program effects on knowledge, behaviour and skills of students and teachers also compared schools that have implemented the adiwiyata program with schools that have not implemented adiwiyata program. This study is a quantitative descriptive research. The subjects were students and teachers of SMK Negeri 1 Pangkalan Kerinci and SMK Negeri 1 Bunut with total 194 people. The data collection methode used were questionnaires, interviews and observations, data analysis technique using Chi-square test with SPSS version 20 for windows. Results of the study Chi Square test showed between SMK 1 Pangkalan Kerinci with SMKN 1 Bunut about students' knowledge Chi Square count 140.437 and Chi Square table 101.879, student behavior Chi Square count 102.920 and Chi Square tables 101.879 and attitudes Chi Square count 101 994 and Chi Square tables 101.879. Knowledge, attitudes and skills of teachers Chi Square test results Chi Square count of 10,000 and Chi Square Table 18.307. It can be concluded that the existence of a significant difference of knowledge, attitudes and skills of students between SMK 1 Pangkalan Kerinci with SMKN 1 Bunut, because the value of Chi Square count is greater than the value of Chi Square table and there was no significant difference about knowledge, attitudes and skills teacher between SMKN 1 Pangkalan Kerinci with SMKN 1 Bunut, because there is a calculated value of Chi Square is smaller than the value of Chi Square table.