Physical Sciences and Mathematics Commons^™

In many disciplines of social sciences, it’s widely believed that main effect is uninterpretable when moderation exists. This research starts with an observation that four popular mode of data analysis, mediation, moderation,

curvilinearity, and confounding, all attempt to dissect an XY simple linear effect into various components.

Through this prism of theory, this research uncovers an important interpretation for the main effect, with or without moderation. The main effect, according to the theory of causal dissection, is a combination of two effects, namely on‐group effect and in‐group effect, while the in‐group effect is a weighted average of the XY effects …

Statistical significance test, one of the most important contributions of mathematical statistics, was designed for projection, namely to project from a sample to its population, by estimating the probability (p) that a difference

observed in a probability sample does not exist in the population from which the sample has been drawn. In social sciences, however, researchers have used the significance tests for three other functions, namely proof, prescreen, and prototyping.