Lack of replicability of scientific discoveries has surfaced too often in recent years, and even reached the attention of the general public. An ignored cause is the inappropriate statistical treatment of two statistical problems: (1) selective inference, manifested in selecting few promising leads following the statistical analysis of the potential many, where ignoring the selection process on estimates, confidence intervals and observed significance; (2) using too optimistic a yardstick of variation with which confidence intervals set and statistical significance of the potential discovery is judged, as a result of ignoring the variability between laboratories and subjects. The first problem becomes more serious as the pool of potential discoveries increases, the second paradoxically becomes more serious as measuring ability improves, which explain why the two problems are more prominent in recent years. Both problems have statistical solutions, but the solutions are not practical as they burden the analysis to a point where the power to discover new findings is exceedingly low. Therefore, unless required by regulating agencies, scientists tend to avoid using these solutions.I propose to develop methods that address such replicablity problems specific to medical research, epidemiology, genomics, brain research, and behavioral neuroscience. The methods include (a) new hierarchical weighted procedures, and model selection methods, that control the false discovery rate in testing; (b) shorter confidence intervals that offer false coverage-statement rate for the selected, both addressing the concern about selective inference; and (c) a compromise between using random effects models for the laboratories and subjects and treating them as fixed, to be aided by multiple laboratory database in behavior genetics and neuroscience. By serving the exact needs of scientists, while avoiding excessive protection, I expect the offered methodologies to become widely adapted.