Multiple testing problems are ubiquitous in clinical and scientific investigations, from testing multiple endpoints in clinical trials, to examining hundreds of thousands of brain voxels in brain imaging research and millions of single nucleotide polymorphisms (SNPs) in genetic studies. Central to multiple testing is to control for the type I error. The behavior of multiple testing procedures for alpha-control when the tests are independent or dependent but with a known joint distribution is relatively well known. When the joint distribution of test statistics is unknown, one can still guarantee the $\alpha$-control, if the positive dependency through stochastic ordering (PDS) condition is satisfied. Despite the frequent occurrence of unknown test dependency in multiple testing and the importance of the PDS condition in endorsing its validity, little do we know about how to verify the condition. Here, we develop a new nonparametric statistical test, called the CoCo test, based on ranked correlation coefficients and a simple, yet effective, algebraic arrangement of the Spearman's rho and Kendall's tau, that can validate the condition of PDS, through which one can control for alpha regardless of the prior knowledge of the dependency between test statistics. Simulation studies show that the CoCo test can faithfully detect the violation of the PDS condition or lack thereof. To further evaluate the efficacy of the CoCo test, we apply it to investigate two meta-analyses: 72 trials on patients with metastatic breast cancer and 12 trials on patients with advanced solid tumors. Our simulation studies and data analyses strongly encourage one to evaluate the PDS condition during multiple testing, especially when one is uncertain about the relationship between tests, and the proposed CoCo test provides both methodological insights into and a technical device for doing so. An R package cocotest to implement the proposed methodology is available at CRAN.