  We study the sensitivity of the methods available for abundance
determinations in H II regions to potential observational problems. We compare
the dispersions they introduce around the oxygen and nitrogen abundance
gradients when applied to five different sets of spectra of H II regions in the
galaxy M81. Our sample contains 116 H II regions with galactocentric distances
of 3 to 33 kpc, including 48 regions observed by us with the OSIRIS long-slit
spectrograph at the 10.4-m Gran Telescopio Canarias telescope. The direct
method can be applied to 31 regions, where we can get estimates of the electron
temperature. The different methods imply oxygen abundance gradients with slopes
of -0.010 to -0.002 dex kpc-1, and dispersions in the range 0.06-0.25 dex. The
direct method produces the shallowest slope and the largest dispersion,
illustrating the difficulty of obtaining good estimates of the electron
temperature. Three of the strong-line methods, C, ONS, and N2, are remarkably
robust, with dispersions of ~ 0.06 dex, and slopes in the range -0.008 to
-0.006 dex kpc-1. The robustness of each method can be directly related to its
sensitivity to the line intensity ratios that are more difficult to measure
properly. Since the results of the N2 method depend strongly on the N/O
abundance ratio and on the ionization parameter, we recommend the use of the C
and ONS methods when no temperature estimates are available or when they have
poor quality, although the behaviour of these methods when confronted with
regions that have different properties and different values of N/O should be
explored.
