A relationship is derived between power anisotropy and wavevector anisotropy in turbulent fluctuations. This can be used to interpret plasma turbulence measurements, for example, in the solar wind. If fluctuations are spatially anisotropic, then the ion gyroscale break point in measured spectra in the directions parallel and perpendicular to the magnetic field would not occur at the same frequency, and similarly for the electron gyroscale break point. This is an important consideration when interpreting solar wind measurements in terms of anisotropic turbulence theories. Model magnetic field power spectra are presented assuming a cascade of critically balanced Alfvén waves in the inertial range and kinetic Alfvén waves in the dissipation range. The variation of power anisotropy with scale is compared to existing solar wind measurements, and the similarities and differences are discussed.