  Close binaries suppress the formation of circumstellar (S-type) planets and
therefore significantly bias the inferred planet occurrence rates and
statistical trends. After compiling various radial velocity and high-resolution
imaging surveys, we determine that binaries with a < 1 au fully suppress S-type
planets, binaries with a = 10 au host close planets at 15% the occurrence rate
of single stars, and wide binaries with a > 200 au have a negligible effect on
close planet formation. We show that F = 43% +/- 7% of solar-type primaries do
not host close planets due to suppression by close stellar companions. By
removing spectroscopic binaries from their samples, radial velocity surveys for
giant planets boost their detection rates by a factor of 1/(1-F) = 1.8 +/- 0.2
compared to transiting surveys. This selection bias fully accounts for the
discrepancy in hot Jupiter occurrence rates inferred from these two detection
methods. Correcting for both planet suppression by close binaries and transit
dilution by wide binaries, the occurrence rate of small planets orbiting single
G-dwarfs is 2.1 +/- 0.3 times larger than the rate inferred from all G-dwarfs
in the Kepler survey. Additionally, about half (but not all) of the observed
increase in small, short-period planets toward low-mass hosts can be explained
by the corresponding decrease in the binary fraction. Finally, we demonstrate
that the apparent enhancement of wide stellar companions to hot Jupiter hosts
is due to multiple selection effects. Very close binaries, brown dwarf
companions, and massive planets with M_2 > 7 M_J within a < 0.2 au
preferentially have metal-poor hosts and wide tertiary companions, but genuine
hot Jupiters with M_p = 0.2-4 M_J that formed via core accretion instead favor
metal-rich hosts and do not exhibit a statistically significant excess of wide
stellar companions.
