Triangular contingency tables are a special class of incomplete contingency tables. Association and independence models are used to analyze such tables. Association models can be described in terms of the association parameters for the analysis of triangular contingency tables having ordered categories. The aim of this study is to show the relation between the association parameters of the uniform association model and the sample correlation coefficient under the structural zeros. For this purpose, a simulation study based on random contingency tables containing structural zeros is performed. Association parameters are estimated under the uniform association models. The sample correlation coefficients are computed using these parameter estimates and compared with the population correlation coefficients. It is shown that by using the association parameter estimates under the uniform association model, better estimates can be achieved for the population correlation coefficient in the case of structural zeros.