Hayashi, Y., 1982: Confidence intervals of a climatic signal. Journal of the Atmospheric Sciences, 39 (9), 1895-1905.

Abstract: In order to interpret climate statistics correctly, the definitions of climate change, signal-to-noise ratio and statistical significance are clarified.
It is proposed to test the significance of climate statistics by the use of confidence intervals, since they are more informative than merely testing the null hypothesis that the true response is zero. The confidence intervals of the mean difference, variance ratio and signal-to-noise ratio are formulated and applied to a climate sensitivity study.
It is also proposed to make a multivariate test of a response pattern by the use of joint confidence intervals, since they are more informative than merely testing the null hypothesis that the true response is everywhere zero. These intervals can also be applied to test the joint significance of the amplitude and phase of the seasonal cycles of a response.