An examination of the period-V amplitude relation for RRab stars (fundamental mode pulsators) with `normal light curves in the Oosterhoff type I clusters M3 and M107 and in the Oosterhoff type II clusters M9 and M68 reveals that the V amplitude for a given period is not a function of metal abundance. Rather, it is a function of the Oosterhoff type. This result is confirmed by published observations of RRab stars in M4, M5 and M92. A method devised by Jurcsik and Kovacs has been used to determine whether the light curve of an RRab star is `normal or `peculiar. Although M3 is considered to belong to the Oosterhoff type I group, it has three bright RRab stars that seem to fit the period-amplitude relation for Oosterhoff type II RRab stars. There is evidence that these bright stars are in a more advanced evolutionary state than the other RRab stars in M3, thus leading to the conclusion that the Oosterhoff dichotomy is due to evolution. Our result gives support to the Lee, Demarque & Zinn hypothesis that most RR Lyrae variables in Oosterhoff type I clusters are ZAHB objects while those in the Oosterhoff type II clusters are more evolved. This may have important implications for the derived ages of Oosterhoff type II clusters. If their RR Lyrae variables have all evolved away from the ZAHB, then their ages have been overestimated in studies that assume they are ZAHB objects.
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