The paper by Robert E. Livezee and W. Y. Chen addresses the significant impact of the number and interdependence of statistics on the collective significance of finite sets, particularly in spatial networks of time-averaged meteorological data. The authors propose a two-step approach to evaluate the significance of such data: first, prescreening for significance assuming data independence, and second, considering dependence through estimated effective degrees of freedom and the binomial distribution or Monte Carlo simulation. Seasonal averages of 700 mb height data are used to illustrate these methods. The authors critically examine three recent papers (Hancock and Yarger, Naström and Belmont, Williams) in light of these considerations and suggest Monte Carlo strategies to clarify ambiguities. They argue that the statistical significance of results in these studies is often overstated and propose specific Monte Carlo tests to resolve any residual uncertainties. The paper also discusses the theoretical and empirical considerations for evaluating the finiteness and interdependence of statistics, emphasizing the importance of accounting for spatial correlation and the use of Monte Carlo simulation. The authors provide examples and detailed analyses to demonstrate the effectiveness of their proposed methods. Finally, the paper concludes by discussing the potential extension of these techniques to the significance testing of general circulation model (GCM) sensitivity tests, suggesting that Monte Carlo approaches could be particularly useful in this context.The paper by Robert E. Livezee and W. Y. Chen addresses the significant impact of the number and interdependence of statistics on the collective significance of finite sets, particularly in spatial networks of time-averaged meteorological data. The authors propose a two-step approach to evaluate the significance of such data: first, prescreening for significance assuming data independence, and second, considering dependence through estimated effective degrees of freedom and the binomial distribution or Monte Carlo simulation. Seasonal averages of 700 mb height data are used to illustrate these methods. The authors critically examine three recent papers (Hancock and Yarger, Naström and Belmont, Williams) in light of these considerations and suggest Monte Carlo strategies to clarify ambiguities. They argue that the statistical significance of results in these studies is often overstated and propose specific Monte Carlo tests to resolve any residual uncertainties. The paper also discusses the theoretical and empirical considerations for evaluating the finiteness and interdependence of statistics, emphasizing the importance of accounting for spatial correlation and the use of Monte Carlo simulation. The authors provide examples and detailed analyses to demonstrate the effectiveness of their proposed methods. Finally, the paper concludes by discussing the potential extension of these techniques to the significance testing of general circulation model (GCM) sensitivity tests, suggesting that Monte Carlo approaches could be particularly useful in this context.