A main theme in causal mediation analysis is to study various types of causal effects. However, their statistical effects are understudied. There are findings that the size of the causal effects seems to be unrelated to the size of their statistical effects, resulting some power anomalies. Using the joint likelihood of the mediator and the outcome, various statistical effects a treatment has on the outcome are tested using likelihood ratio tests (LRTs). The size of each effect is measured by the non-centrality of its LRT. The LRTs for the indirect effect and the total effect are intersection-union tests. The test of the indirect effect, when the Wald statistics are used in place of the LRTs, is shown to be more powerful than the Sobel test. This framework provides a theoretical foundation for the current trend that abandons the first step and retains the second and the third steps of Baron-Kenny's four steps for mediation analysis. It accommodates a wide range of models on the mediator and the outcome. Data examples with continuous, binary, and survival outcomes are presented.