Anti-Diagonals-Parameter Symmetry Model for Square Contingency Tables with Ordinal Classifications

For analyzing square tables having same row and column classifications, analysts are often interested in whether or not the relation between the row and column variables is symmetric or asymmetric regarding the main-diagonal cells of the table. However, for the dataset of grip strength test, analysts may be interested in whether or not the relation of them is symmetric or asymmetric regarding the anti-diagonal cells, instead of the main-diagonal cells. This study proposes the anti-diagonals-parameter symmetry model that represents the asymmetric structure regarding the anti-diagonal cells. Furthermore, this study provides a separation of the anti-symmetry model using the anti-diagonals-parameter symmetry model and an orthogonal separation of the test statistic for the anti-symmetry model. This study shows the advantages of the anti-diagonals-parameter symmetry model by applying it to the real-dataset of grip strength test.