Analysis of the Grip Strength Data Using Anti-Diagonal Symmetry Models

Kiyotaka Iki

doi:10.4236/ojs.2016.64049

Abstract

For the analysis of square contingency tables with the same row and column ordinal classifications, this article proposes new models which indicate the structures of symmetry with respect to the anti-diagonal of the table. Also, this article gives a simple decomposition in 3 ′ 3 contingency table using the proposed models. The proposed models are applied to grip strength data.

Highlights

The present paper proposes three models and gives a simple decomposition using the proposed models in 3× 3 contingency table
We shall refer to this model as the anti-diagonal symmetry (AS) model
We shall refer to this model as the anti-diagonal global symmetry (AGS) model

Summary

Introduction

For such data with similar classifications, many observations tend to fall (or near) the main diagonal cells. Model states that the probability that an observation will fall in the (i,j)th cell of the table is equal to the probability that it falls in the (j,i)th cell This model describes a structure of symmetry with respect to the main diagonal of the table.

New Models and a Simple Decomposition

An Example

Concluding Remarks