We estimate the H i intensity fluctuation power spectrum for a sample of 18 spiral galaxies chosen from THINGS .
Our analysis spans a large range of length-scales from \sim 300 { pc } to \sim 16 { kpc } across the entire galaxy sample .
We find that the power spectrum of each galaxy can be well fitted by a power law P _ { HI } ( U ) = A U ^ { \alpha } , with an index \alpha that varies from galaxy to galaxy .
For some of the galaxies the scale-invariant power-law power spectrum extends to length-scales that are comparable to the size of the galaxy ’ s disk .
The distribution of \alpha is strongly peaked with 50 \% of the values in the range \alpha = -1.9 to 1.5 , and a mean and standard deviation of -1.3 and 0.5 respectively .
We find no significant correlation between \alpha and the star formation rate , dynamical mass , H i mass or velocity dispersion of the galaxies .

Several earlier studies that have measured the power spectrum within our Galaxy on length-scales that are considerably smaller than 500 { pc } have found a power-law power spectrum with \alpha in the range \approx - 2.8 to -2.5 .
We propose a picture where we interpret the values in the range \approx - 2.8 to -2.5 as arising from three dimensional ( 3D ) turbulence in the Interstellar Medium ( ISM ) on length-scales smaller than the galaxy ’ s scale-height , and we interpret the values in the range \approx - 1.9 to -1.5 measured in this paper as arising from two-dimensional ISM turbulence in the plane of the galaxy ’ s disk .
It however still remains a difficulty to explain the small galaxy to galaxy variations in the values of \alpha measured here .