The authors investigate two measures of the effective number of spatial degrees of freedom (ESDOF) for time-varying fields. The first measure, based on matching the mean and variance of the spatially integrated squared anomaly to a chi-squared distribution, and the second, based on EOF variance partitioning, are shown to be useful for assessing field significance. These measures are compared to traditional EOF methods and are found to be effective in different contexts. The first measure, called moment-matching (N_mm*), is based on the first two moments of the spatially integrated variance, while the second, called eigenvalue formula (N_ef*), is based on the eigenvalues of the covariance matrix. Both measures are shown to be sensitive to non-normality of the data and the length of the time record. The authors also discuss the relationship between ESDOF and effective sample size for autocorrelated time series and show that ESDOF can be used to assess the significance of correlations between two time series. The paper concludes that ESDOF is a useful tool for assessing field significance and that it can be used in a variety of contexts, including statistical significance testing of correlations between two time series. The authors also show that ESDOF can be used to assess the significance of differences between two realizations of a field and that it is a useful tool for assessing the significance of field covariance and correlation. The paper also discusses the limitations of ESDOF in cases of non-normal data and the importance of choosing an appropriate value of ESDOF for a given test. The authors conclude that ESDOF is a valuable tool for assessing field significance and that it can be used in a variety of contexts, including statistical significance testing of correlations between two time series.The authors investigate two measures of the effective number of spatial degrees of freedom (ESDOF) for time-varying fields. The first measure, based on matching the mean and variance of the spatially integrated squared anomaly to a chi-squared distribution, and the second, based on EOF variance partitioning, are shown to be useful for assessing field significance. These measures are compared to traditional EOF methods and are found to be effective in different contexts. The first measure, called moment-matching (N_mm*), is based on the first two moments of the spatially integrated variance, while the second, called eigenvalue formula (N_ef*), is based on the eigenvalues of the covariance matrix. Both measures are shown to be sensitive to non-normality of the data and the length of the time record. The authors also discuss the relationship between ESDOF and effective sample size for autocorrelated time series and show that ESDOF can be used to assess the significance of correlations between two time series. The paper concludes that ESDOF is a useful tool for assessing field significance and that it can be used in a variety of contexts, including statistical significance testing of correlations between two time series. The authors also show that ESDOF can be used to assess the significance of differences between two realizations of a field and that it is a useful tool for assessing the significance of field covariance and correlation. The paper also discusses the limitations of ESDOF in cases of non-normal data and the importance of choosing an appropriate value of ESDOF for a given test. The authors conclude that ESDOF is a valuable tool for assessing field significance and that it can be used in a variety of contexts, including statistical significance testing of correlations between two time series.