Uneven and changing spatial distributions of air temperature stations can produce unrepresentative samples of the space-time variability of near-surface air temperature. Over the last century, station networks have varied from less than 300 stations that are largely limited to the Northern Hemisphere to nearly 1700 stations that are fairly well distributed over the terrestrial surface. As a result, estimates of air temperature change derived from historical observation networks often contain network-induced variability. Spatial resampling methods are used to estimate network-induced variability in terrestrially averaged air temperature anomalies and trends. Random resampling from the station networks allows pseudo confidence intervals and other statistics of variability to be estimated. Network-induced variability appears to be substantial during the late 1800s, especially in the Southern Hemisphere. Most networks from the 1900s and the Northern Hemisphere, however, appear to produce reliable estimates of spatially averaged air temperature anomalies and trends. A non-random, but historically appropriate, resampling method - sampling a given year's air temperature anomaly field using another year's station distribution - also is used. Using 1987 - one of the warmest years on record - as an example, station distributions from 1881-1988 are used to sample the 1987 air temperature anomaly field. This sampling procedure produces spatially averaged air temperature anomalies for 1987 that vary by over 0.3°C. A combinatorial process of resampling a given year's anomaly field is repeated for every year and every station network to produce terrestrial average air temperature anomaly estimates that vary by more than 0.3°C solely due to network changes.