Statistical tools based on the maximal overlap discrete wavelet transform (MODWT) are reviewed, and then applied to a dataset of aircraft observations of the atmospheric boundary layer from the tropical eastern Pacific, which includes quasi-stationary and non-stationary segments. The wavelet methods provide decompositions of variances and covariances, e.g. fluxes, between time scales that effectively describe a broadband process like atmospheric turbulence. Easily understood statistical confidence bounds are discussed and applied to these scale decompositions, and results are compared to Fourier methods for quasi-stationary turbulence. The least asymmetric LA(8) wavelet filter yields coefficients that exhibit better uncorrelatedness across scales than the Haar filter and is better suited for decomposition of broadband turbulent signals. An application to a non-stationary segment of our dataset, namely vertical profiles of the turbulent dissipation rate, highlights the flexibility of wavelet methods.