  Several model-independent parameterizations of deviations from General
Relativity have been developed to test Einstein's theory. Although these
different parameterizations were developed for different gravitational
observables, they ultimately all test the same underlying physics. In this
paper, we develop connections between the parameterized post-Newtonian,
parameterized post-Keplerian, and the parameterized post-Einsteinian
frameworks, developed to carry out tests of General Relativity with Solar
System, binary pulsar, and gravitational wave observations respectively. These
connections allow us to use knowledge gained from one framework to inform and
guide tests using the others. Relating these parameterizations and combining
the results from each approach strengthens our tests of General Relativity.
