Tree-based paleobiological studies use inferred phylogenies as models to test hypotheses about macroevolution and the quality of the fossil record. Such studies raise two concerns. The first is how model trees might bias results. The second is testing hypotheses about parameters that affect tree inference.Bias introduced by model trees is explored for tree-based assessments of the quality of the fossil record. Several nuisance parameters affect tree-based metrics, including consistency of sampling probability, rates of speciation/extinction, patterns of speciation, applied taxonomic philosophy, and assumed taxonomy. The first two factors affect probabilistic assessments of sampling, but also can be tested and accommodated in sophisticated probability tests. However, the final three parameters (and the assumption of a correct phylogeny) do not affect probabilistic assessments.Often paleobiologists wish to test hypotheses such as rates of character change or rates of preservation. Assumptions about such parameters are necessary in simple phylogenetic methods, even if the assumptions are that rates are homogeneous or that sampling is irrelevant. Likelihood tests that evaluate phylogenies in light of stratigraphic data and/or alternative hypotheses of character evolution can reduce assumptions about unknowns by testing numerous unknowns simultaneously. Such tests have received numerous criticisms, largely based in philosophy. However, such criticisms are based on incorrect depictions of the logical structures of parsimony and likelihood, misunderstandings about when arguments are probabilistic (as opposed to Boolean), overly restrictive concepts of when data can test a hypothesis, and simply incorrect definitions of some terms.Likelihood methods can test multiparameter hypotheses about phylogeny and character evolution (i.e., rates, independence, etc.). The best hypothesis positing a single rate of independent character change (with no variation among character states) is determined for each topology. Hypotheses about rate variation among characters or across phylogeny, character independence, and different patterns of state evolution then are examined until one finds the simplest (i.e., fewest varying parameters) hypothesis that cannot be rejected given knowledge of a more complicated hypothesis. This is repeated for alternative topologies. An example is presented using hyaenids. Two trees are contrasted, one of which requires the minimum necessary steps and the other of which requires at least seven additional steps. Given either tree, likelihood rejects fewer than three general rates of character change and also rejects the hypothesis of independence among the characters. However, hypotheses of changes in rates across the tree do not add substantially to the tree likelihood. The likelihoods of the trees given stratigraphic data also are determined. Both morphologic and stratigraphic data suggest that the multiparameter hypothesis including the parsimony tree is significantly less likely than the multiparameter hypothesis including a different tree.