  We consider the distribution of normalized Frobenius traces for two families
of genus 3 hyperelliptic curves over Q that have large automorphism groups:
y^2=x^8+c and y^2=x^7-cx with c in Q*. We give efficient algorithms to compute
the trace of Frobenius for curves in these families at primes of good
reduction. Using data generated by these algorithms, we obtain a heuristic
description of the Sato-Tate groups that arise, both generically and for
particular values of c. We then prove that these heuristic descriptions are
correct by explicitly computing the Sato-Tate groups via the correspondence
between Sato-Tate groups and Galois endomorphism types.
