Inference statistical analysis of continuous data based on confidence bands-Traditional and new approaches

In the analysis of continuous data, researchers are often faced with the problem that statistical methods developed for single-point data (e.g., t test, analysis of variance) are not always appropriate for their purposes. Either methodological adaptations of single-point methods will need to be made, or confidence bands are the method of choice. In this article, we compare three prominent techniques to analyze continuous data (single-point methods, Gaussian confidence bands, and function-based resampling methods to construct confidence bands) with regard to their testing principles, prerequisites, and outputs in the analysis of continuous data. In addition, we introduce a new technique that combines the advantages of the existing methods and can be applied to a wide range of data. Furthermore, we introduce a method enabling a priori and a posteriori power analyses for experiments with continuous data.