Abstract: This study proposes a measure of the strength of association, agreement or concordance between state of nature or condition in a population and test results in diagnostic screening tests. The proposed measure here termed S coefficient of concordance because it is a function of the sensitivity and specificity of the screening test is normal between 0 and 1, assuming the value 0 when there is independence, complete discordance or disagreement and the value 1 when there is complete agreement or similarity between state of nature or condition and test results. Unlike the traditional odds ratio, the proposed S statistic in its specification and formulation properly ensures the non inclusion of the number of subjects in the sampled population who test negative, even though they are actually positive in nature and the number of subjects who test positive, even though they actually do not have the condition in nature, since these numbers are usually not known in diagnostic screening tests. The method develops the standard deviation of the proposed measure as well as test statistics that enables the testing of any desired hypothesis about not only the proposed S measure but also the sensitivity and specificity of the screening test. The method is illustrated with some sample data and the proposed S measure is shown to be relatively more efficient and hence likely to be more powerful than the traditional odds ratio measure of association.