Methods to simultaneously select for yield and stability need to be compared to determine which index is the best choice to identify high-yielding, stable genotypes. A comparison of the repeatability of different measures of stability would be useful because stability statistics with high repeatability should be superior to identify stable genotypes. Stability measures were evaluated for 116 oat (Avena sativa L.) lines in 36 Iowa environments. The objectives were (i) to evaluate the mean selection differential when selection was for yield, stability statistics, or simultaneous selection for both yield and stability, using different indices; (ii) to compare repeatability of the stability regression (b(i)) stability variance component (sigma(i)2), and deviation from regression mean square (sd(i)2) across random subsets of 18 environments; and (iii) to estimate rank correlations between stability statistics and mean grain yield, in all environments. Simultaneous selection for yield and stability, based on three indices, identified high-yielding, stable genotypes. Selection solely for yield identified genotypes with high mean yield that on average were not stable. Selection solely for each stability measure identified genotypes with low yield that were stable. The repeatability of b(i) was 0.61, and the index that used this measure of stability combined with selection for yield identified 12 genotypes that yielded 3% less than the average of the highest yielding 12 genotypes. Repeatability of sigma(i)2 was 0.28 and repeatability of sd(i)2 was 0.17. The correlation between yield and b(i) was 0.73, between yield and sigma(i)2 was 0.21, and between yield and sd(i)2 was 0.28.