The overspeeding is a bias on the mean-wind velocity. However, a cup anemometer can be sampled with so high a rate that it is possible to determine higher-order moments. It is therefore useful to know if these moments are bias free. A rather complicated theoretical analysis shows they actually are. This is documented by field measurements where the signals from a cup anemometer and a sonic anemometer are used to compute second, third,-and fourth order moments. Also skewness and kurtosis are determined form the data and compared. It is quite obvious that there is a statistical spread, in particular for the highest moments. But there is no discernible bias.