The statistical reliability of ice thickness distributions derived from submarine sonar data sets of finite length is examined, focusing on the standard error ϵH(L) in the mean ice draft H derived from a record of length L km. This is important in assessing the significance or otherwise of quoted temporal or spatial differences in mean ice draft. Estimates for ϵH(50) are derived from four different submarine surveys, each of which involved repeated sampling of apparently homogeneous ice fields. Values ranged from 7.18 to 15.29% of the mean; for climate-related comparisons of data sets from different years in the same location a value of 12.75% is recommended, derived from data gathered at the north pole. This value is used to reassess the significance of published data on ice draft variability; quoted variability at the north pole over the 1977--1990 period is found to be not statistically significant, but a difference in area/averaged ice draft over the Eurasian Basin between 1976 and 1987 remains highly significant. Using hitherto unreported 1987 data from the north pole area, the statistical variability of other parameters of the ice cover is examined. The frequency of lead occurrence, the width of leads, the fractional cover of smooth ice, and the frequency of keel occurrence all show standard errors of 22--24% in their mean values, while mean keel draft has a 4% error, all over a 50-km track length. Finally, unreported 1987 data, for an area extending from the pole to 72 ¿N along the prime meridian and the East Greenland shelf break, are examined in 1¿ bins, using ϵH(L) to assess the significance of variations in the mean. A statistically significant decline in mean ice draft is observed, starting at 86 ¿N and continuing to 72 ¿N; a linear regression gives a thinning rate of 0.22 m/deg. The decline within the Arctic Basin itself is tentatively ascribed to a mixture of under-ice melt and mixing of ice types, since data on young ice occurrence show that divergence did not occur north of Fram Strait. ¿ 1997 American Geophysical Union