PMC:4620161 / 33420-34591 JSONTXT

{"target":"http://pubannotation.org/docs/sourcedb/PMC/sourceid/4620161","sourcedb":"PMC","sourceid":"4620161","source_url":"https://www.ncbi.nlm.nih.gov/pmc/4620161","text":"The geometrical interpretations of the hypotheses are the following (Table 1). EXC (9a) tests the main effect (or first-way interaction) of Component, representing a straight line in ℝm. The associated test for (9a) is executed on the distance between the data line and the null line (a diagonal line through the origin). As the correct null hypothesis (2a) is only a subset of H01EXC, its rejection domain is only a subset of the rejection domain for MVT (2a), leading to a misrepresentation in (9a) and a detection failure when the group centroid lies on the null line but not at the origin (i.e., the HDR curve is roughly a flat line). Similarly, EXC (9b) as a two-way interaction between Group/Condition and Component is represented by two lines, and the corresponding test acts on the distance between the two lines: are the HDR profiles parallel with each other between the two groups or conditions? As the correct null hypothesis (2b) is only a subset of EXC (9b), the rejection domain of EXC (9b) is only a subset of MVT (2b), resulting in a misrepresentation in (9b) and a detection failure when the two HDR curves are roughly parallel with each other (Table 1).","tracks":[]}