Overlapping confidence intervals or standard error intervals: what do they mean in terms of statistical significance?

We investigate the procedure of checking for overlap between confidence intervals or standard error intervals to draw conclusions regarding hypotheses about differences between population parameters. Mathematical expressions and algebraic manipulations are given, and computer simulations are performed to assess the usefulness of confidence and standard error intervals in this manner. We make recommendations for their use in situations in which standard tests of hypotheses do not exist. An example is given that tests this methodology for comparing effective dose levels in independent probit regressions, an application that is also pertinent to derivations of LC50s for insect pathogens and of detectability half-lives for prey proteins or DNA sequences in predator gut analysis.