The paper discusses the statistical significance of finite sets of meteorological data, emphasizing the importance of considering both the number of data points and their interdependence. It argues that traditional methods often fail to account for these factors, leading to overestimation of significance. The authors propose a two-step testing procedure: first, using binomial distributions to assess significance assuming independence, and second, using Monte Carlo simulations to account for spatial dependence. The paper critiques recent studies, including those by Hancock and Yarger, Williams, and Nastrom and Belmont, for not properly accounting for spatial correlation and interdependence, leading to potentially overstated significance levels. It demonstrates that Monte Carlo simulations can accurately assess significance by simulating random data and comparing results to the observed data. The authors use examples from seasonal 700 mb height data to illustrate the problem. They show that when spatial dependence is considered, the required number of significant points for significance at the 95% level is much higher than when independence is assumed. This highlights the importance of accounting for spatial correlation in significance testing. The paper also discusses the limitations of traditional statistical tests in the presence of spatial correlation and the need for Monte Carlo simulations to accurately assess significance. It concludes that Monte Carlo techniques are essential for evaluating the significance of climate data, particularly in the context of general circulation model (GCM) sensitivity tests. The authors suggest that Monte Carlo simulations can be used to assess the significance of differences between undisturbed and disturbed GCM climates, taking into account spatial and variable correlations.The paper discusses the statistical significance of finite sets of meteorological data, emphasizing the importance of considering both the number of data points and their interdependence. It argues that traditional methods often fail to account for these factors, leading to overestimation of significance. The authors propose a two-step testing procedure: first, using binomial distributions to assess significance assuming independence, and second, using Monte Carlo simulations to account for spatial dependence. The paper critiques recent studies, including those by Hancock and Yarger, Williams, and Nastrom and Belmont, for not properly accounting for spatial correlation and interdependence, leading to potentially overstated significance levels. It demonstrates that Monte Carlo simulations can accurately assess significance by simulating random data and comparing results to the observed data. The authors use examples from seasonal 700 mb height data to illustrate the problem. They show that when spatial dependence is considered, the required number of significant points for significance at the 95% level is much higher than when independence is assumed. This highlights the importance of accounting for spatial correlation in significance testing. The paper also discusses the limitations of traditional statistical tests in the presence of spatial correlation and the need for Monte Carlo simulations to accurately assess significance. It concludes that Monte Carlo techniques are essential for evaluating the significance of climate data, particularly in the context of general circulation model (GCM) sensitivity tests. The authors suggest that Monte Carlo simulations can be used to assess the significance of differences between undisturbed and disturbed GCM climates, taking into account spatial and variable correlations.