  Current concerns regarding the dependability of psychological findings call
for methodological developments to provide additional evidence in support of
scientific conclusions. This paper highlights the value and importance of two
distinct kinds of parameter uncertainty which are quantified by confidence sets
(CSs) and fungible parameter estimates (FPEs); both provide essential
information regarding the defensibility of scientific findings. Using the
structural equation model, we introduce a general perturbation framework based
on the likelihood function that unifies CSs and FPEs and sheds new light on the
conceptual distinctions between them. A targeted illustration is then presented
to demonstrate the factors which differentially influence CSs and FPEs, further
highlighting their theoretical differences. With three empirical examples on
initiating a conversation with a stranger, posttraumatic growth of caregivers
in the context of pediatric palliative care, and the direct and indirect
effects of spirituality on thriving among youth, we illustrate how CSs and FPEs
provide unique information which lead to better informed scientific
conclusions. Finally, we discuss the importance of considering information
afforded by CSs and FPEs in strengthening the basis of interpreting statistical
results in substantive research, conclude with future research directions, and
provide example OpenMx code for the computation of CSs and FPEs.
