We present a test for the degree of symmetry in the distribution of the Hα brightness along the arms of a sample of spiral galaxies. The test consists of deriving the cross-correlation function of the Hα brightness as a function of curvilinear distance along pairs of opposed arms, after unfolding the arms geometrically. Our results reveal a significantly greater degree of symmetry in the non-barred population than in the barred. We derive parameters for both bar strength and bar ellipticity, and compare these with the derived cross-correlations to strengthen this conclusion. We suggest that density waves are a probable cause for the appearance of global, i.e. disc-wide, two-fold symmetry in spiral discs. Comparison with published work on abundance gradients in the discs of barred and non-barred galaxies indicates that, as for the abundances, mixing in the spiral disc as a result of the bar potential may well be responsible for our observation that stronger bars are related to reduced two-fold symmetry in the distribution of star-forming regions along the spiral arms.