  We measure nonlocal third-order spatial correlations in non-degenerate
ultracold gases of bosonic ($^{84}$Sr) and spin-polarized fermionic ($^{87}$Sr)
strontium through studies of the formation rates for ultralong-range trimer
Rydberg molecules. The trimer production rate is observed to be very sensitive
to the effects of quantum statistics with a strong enhancement of up to a
factor of six (3!) in the case of bosonic $^{84}$Sr due to bunching, and a
marked reduction for spin-polarized fermionic $^{87}$Sr due to anti-bunching.
The experimental results are compared to theoretical predictions and good
agreement is observed. The present approach opens the way to {\it{in situ}}
studies of higher-order nonlocal spatial correlations in a wide array of
ultracold atomic-gas systems.
