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We perform a detailed study of six transiting planetary systems withrelatively bright stars close enough to affect observations of these systems.Light curves are analysed taking into account the contaminating light and itsuncertainty. We present and apply a method to correct the velocity amplitudesof the host stars for the presence of contaminating light. We determine thephysical properties of six systems (WASP-20, WASP-70, WASP-8, WASP-76, WASP-2and WASP-131) accounting for contaminating light. In the case of WASP-20 themeasured physical properties are very different for the three scenariosconsidered (ignoring binarity, planet transits brighter star, and planettransits fainter star). In the other five cases our results are very similar tothose obtained neglecting contaminating light. We use our results to determinethe mean correction factors to planet radius, $\langle X_R\rangle$, mass,$\langle X_M\rangle$, and density, $\langle X_\rho\rangle$, caused by nearbyobjects. We find $\langle X_R\rangle=1.009\pm0.045$, which is smaller thanliterature values because we were able to reject the possibility that theplanet orbits the fainter star in all but one case. We find $\langleX_M\rangle=1.031\pm0.019$, which is larger than $\langle X_R\rangle$ because ofthe strength of the effect of contaminating light on the radial velocitymeasurements of the host star. We find $\langle X_\rho\rangle=0.995\pm 0.046$:the small size of this correction is due to two effects: the corrections onplanet radius and mass partially cancel; and some nearby stars are close enoughto contaminate the light curves of the system but not radial velocities of thehost star. We conclude that binarity of planet host stars is important for thesmall number of transiting hot Jupiters with a very bright and close nearbystar, but it has only a small effect on population-level studies of theseobjects.

A multiplicity study of transiting exoplanet host stars. II. Revised properties of transiting planetary systems with companions