This dissertation focuses on embracing the uncertainty that is associated with multi-step inference. Typically, statistical analyses consist of multiple steps that build on each other and are executed sequentially. Common practice is that each consecutive step ignores the uncertainty of the preceding steps. Throughout this dissertation, it is shown that not embracing uncertainty leads to overconfidence and biased conclusions. Furthermore, I have demonstrated that this uncertainty can be accounted for by averaging across models or by performing the steps that involve uncertainty simultaneously in a single model. For example, instead of averaging the scores from repeated measurements and then analyzing the averages, it is better to directly analyze the unaggregated data. These situations occur with scores given to patients by different raters, as in Chapters 3 and 4, but also with repeated measures ANOVA, as illustrated in Chapters 9 and 10. The discussion suggests several ideas for making the adoption of methods that appropriately account for uncertainty more easily accessible and more standardized. Overall, my hope with this dissertation is that the practice of ignoring uncertainty by tying together several inferential steps becomes a relic of the past and that future studies embrace the uncertainty in the individual steps by adopting multi-model inference
