The root of this problem is that most data sets in psychology, anthropology, and epidemiology are not as large in terms of sample size as what computer scientis

The root of this problem is that most data sets in psychology, anthropology, and epidemiology are not as large in terms of sample size as what computer scientists and electrical engineers encounter. p-values are a surrogate to explicitly describing the data using probability distributions or as random processes. In essence, you sacrifice granularity for simplicity. If you look at the original works of Fisher, etc. and their widespread utility, a large part of early statistics is intended for 'practical statisticians' who seldom encounter data-sets that are 'small' in terms of sample size. As someone who works in electrical engineering/computer science, I've never used the p-value because: 1. The field, in general, demands far more mathematical rigor when dealing with statistics. 2. The demand for mathematical rigor is justified because most data sets we deal with are many orders of magnitude larger than what psychologists and others encounter. So predictions based on limit theorems, etc. are often testable.