Absent randomization, causal conclusions gain strength if several independent evidence factors concur.
We develop a method for constructing evidence factors from several instruments plus a direct comparison
of treated and control groups, and we evaluate the methods performance in terms of design sensitivity
and simulation. In the application, we consider the effectiveness of Catholic versus public high schools,
constructing three evidence factors fromthree past strategies for studying this question, namely: (i) having
nearby access to a Catholic school as an instrument, (ii) being Catholic as an instrument for attending
Catholic school, and (iii) a direct comparison of students in Catholic and public high schools. Although these
three analyses use the same data,we: (i) construct three essentially independent statistical tests of no effect
that require very different assumptions, (ii) study the sensitivity of each test to the assumptions underlying
that test, (iii) examine the degree to which independent tests dependent upon different assumptions
concur, (iv) pool evidence across independent factors. In the application, we conclude that the ostensible
benefit of Catholic education depends critically on the validity of one instrument, and is therefore quite
fragile.