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tokens: Section 3.3 ). A two-sided KolmogorovSmirnov (KS) test on the redshift and i -band magnitude distributions of the matched samples return probabilities of 0.999863 and 0.984483, respectively, thus there is no evidence for rejecting the null hypothesis that the two histograms are drawn from the same underlying distributions of these two observables. Figure 1. The i -band luminosity and redshift ranges for the quasars detected in the FIR at 2 (red points), and the matched sample of quasars undetected at 1 (blue points). The histograms on the bottom and side show the normalized distributions of the respective populations in redshift and L i . Fig. 2 shows the cumulative distributions of C iv blueshift for the FIR-detected and FIR-undetected matched samples. The FIR-detected quasars show larger blueshifts than is expected from their FIR-undetected counterparts, with a two-sided KS test returning a probability that the two distributions are drawn from the same underlying sample of 10 12 . Using 3 and 4 FIR detections instead of the 2 detections, the KS test returns probabilities of 10 8 and 0.0001 that the FIR-detected and FIR-undetected distributions are from the same underlying samples. The 4 sample contains only 140 FIR-detected objects, and thus suffers from the small sample size. Recall that BALQSOs have been removed from the sample, so the difference cannot be attributed to absorbed flux in the blue wing of the emission line. While a nuclear outflow is not always accompanied by a FIR excess, for the sample as a whole, at a given optical luminosity, FIR-bright quasars have larger C iv blueshifts than FIR-undetected quasars. Figure 2. Cumulative distribution of the blueshift of the C iv emission line for the quasars detected in the FIR at 2 (red solid line), and those undetected at 1 (blue dashed line). The FIR-detected quasars have larger C iv blueshifts, indicating more prominent nuclear-driven outflows. The bottom panel shows normalized histograms of the FIR-detected and FIR-undetected C iv blueshifts, in red and blue, respectively. 3.3 Red or reddened quasars Vigorous SF is known to be a dusty process, so if the FIR flux is at least partly from SF, we may expect the FIR-detected quasars to be reddened by dust in the host galaxies, as evidenced by redder optical colours with respect to the general quasar population. Using the same FIR-detected and FIR-undetected matched samples as before, we compare the SDSS g r colours of the two samples. For these luminous quasars, the optical photometry is entirely dominated by emission from the quasar, even if accompanied by a starburst in the host galaxy. To remove the redshift dependence of quasar colours, the colour of an unreddened model quasar similar to that from Maddox etal. ( 2008 ) is subtracted from each object to create a normalized colour. Using the normalized colour, with the redshift dependence removed, creates a distribution that better illustrates departures from the median colour of a