A wide array of atmospheric properties has recently been shown to be correlated to solar activity. The disparate behavior characterizing those properties makes their relationship to solar activity difficult to explain with a unified physical argument. Statistical considerations related to sampling and the length of records available to correlate atmospheric behavior against solar activity are able to explain several of the essential features of solar-atmospheric correlations. Stratifying wintertime data according to the phase of the quasi-biennial oscillation (QBO) leaves undersampled most of the variability in the polar stratosphere operating on quasi-biennial time scales. Aliasing of low frequencies by that undersampled variability introduces spurious covariance that appears to be responsible for the dramatic increase in correlation when data are stratified according to the QBO. Correlations with unstratified data are not explained by aliasing from undersampled behavior. However, uncertainties in their interpretation and reliability leave these quantities open to question as well. The relatively short lengths of atmospheric records limit the ability of cross covariance properties to discriminate to solar activity and hence to distinguish such from other forms of interannual variability. Likewise, the discrete nature of the cross spectrum with solar activity admits only a few statistical degrees of freedom, which limits the reliability with which correlations can be determined. In fact, when the distribution of cross-spectral power is taken into account, none of the correlations considered is significant. Coherence and correlation with sea level pressure both decrease with increasing record length and fall beneath the 90% level of statistical significance when records are extended back to the turn of the 20th century. The physical significance of such properties is considered in statistics generated from artificial solar variability, which demonstrate that behavior like that observed is not unique to the solar period. Over a wide range of period, false solar variability leads to correlations and coherences that are as high or higher than those produced by actual solar variability. A steady increase in these properties with false solar period suggests that time scales typical of solar activity are not represented in the limited atmospheric records adequately enough to permit a reliable calculation of covariance statistics.