How statistical challenges and misreadings of the literature combine to produce unreplicable science: An example from psychology

Given the well-known problems of replicability, how is it that researchers at respected institutions continue to publish and publicize studies that are fatally flawed in the sense of not providing evidence to support their strong claims? We argue that two general problems are: (a) difficulties of analyzing data with multilevel structure and (b) misinterpretation of the literature. We demonstrate with the example of a recently published claim that altering patients' subjective perception of time can have a notable effect on physical healing. We discuss ways of avoiding or at least reducing such problems, including comparing final results to simpler analyses, moving away from shot-in-the-dark phenomenological studies, and more carefully examining previous published claims. Making incorrect choices in multilevel modeling is just one way that things can go wrong, but this example also provides a window into more general problems with complicated designs, cutting-edge statistical methods, and the connections between substantive theory, experimental design, data collection, and replication.