Your ignorance about the relation of significance levels and information speaks volumes. The probability of a Type I error is a function of the level of significance - this conditions the power of the test and the probability of a Tye II error. Most tests in econ research papers test at the 0.05 level - which makes little to no sense in most cases given the data at a researcher's disposal. One of the first things you learn when estimating a linear regression model by least squares, is that a large sample where the explanatory variable is insensitive to changes in the information of the sample implies a large variance in the estimator. The need for quality information that can be extracted from the sample will inevitably lead one to powerful tests. As has been explained to you, these are absent from most tests of hypothesis in economics research. Instead, they rely solely on p-values. This is one the [many] reasons why I (and the majority of people who are educated on the subject) scoff at economists who speak about "results" or "conclusions" in their field.