Figures illustrating the method we used to derive unbiased average luminosity and line ratios (see Sect. 2.5). Upper left panel: probability density distribution of the HCN(5-4) luminosity of our sources determined using a bootstrap technique (Sect. 2.3). The gray filled histogram is the probability distribution of the mean luminosity of our five sources (see Sect. 2.5). The vertical dashed line indicates the zero flux. Upper right panel: same figure for HCO+(5-4). Lower panel: probability density distribution of the ratio between the mean HCN(5-4) and the mean HCO+(5-4) luminosities. The vertical dashed line indicate the median value of the distribution.
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