  We present the first application of a "multiple-tracer" redshift-space
distortion (RSD) analysis to an observational galaxy sample, using data from
the Galaxy and Mass Assembly survey (GAMA). Our dataset is an r < 19.8
magnitude-limited sample of 178,579 galaxies covering redshift interval z < 0.5
and area 180 deg^2. We obtain improvements of 10-20% in measurements of the
gravitational growth rate compared to a single-tracer analysis, deriving from
the correlated sample variance imprinted in the distributions of the
overlapping galaxy populations. We present new expressions for the covariances
between the auto-power and cross-power spectra of galaxy samples that are valid
for a general survey selection function and weighting scheme. We find no
evidence for a systematic dependence of the measured growth rate on the galaxy
tracer used, justifying the RSD modelling assumptions, and validate our results
using mock catalogues from N-body simulations. For multiple tracers selected by
galaxy colour, we measure normalized growth rates in two independent redshift
bins f*sigma_8(z=0.18) = 0.36 +/- 0.09 and f*sigma_8(z=0.38) = 0.44 +/- 0.06,
in agreement with standard GR gravity and other galaxy surveys at similar
redshifts.
