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

Abstract

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.