Heart rate variability (HRV) can be quantified, among others, in the spectral and wavelet domain. The wavelet transform (WT) is an alternative method for the analysis of non-stationary signals. Some recent work shows that the scale-dependent WT standard deviation of the R-R intervals of human ECG can be used to distinguish patients with certain forms of cardiac pathological function from normal subjects. In this paper, we show an explicit relationship between variance of WT and corresponding spectral measure. Also, the statistics of the estimator for variance of WT is obtained. Numerical simulations support the theoretical results. By comparing expected value and variance and spectral measures, we conclude that WT measures are able to diagnose certain cardiac system function.