Where did the p<0.05 criterion come from?
P-value very close to 0.05 means it can go either way. P-value larger than 0.05 indicated weak evidence against the null- hypothesis, so it cannot be rejected. P-value smaller than or equal to 0.05 indicates strong evidence against the null hypothesis, so it should be rejected. Statistics for Dummies, summarizes how p-values are commonly applied and interpreted: Significant or not? The struggle was real. More helpful than this definition, however, is the first of their six principles: “p-values can indicate how incompatible the data are with a specified statistical model.” The definition provided by the ASA’s statement is: “Informally, a p-value is the probability under a specific statistical model that a statistical summary of the data (for example, the sample mean difference between two compared groups) would be equal or more extreme than its observed value”. One of the goals of the statement is to provide a definition of p-value that is straightforward and intuitive, which is not an easy task: An interview among a group of scientists shows that even among the world leading research experts, who could provide a definition of a p-value, it is hard to get a clear interpretation of p-values and statistical significance in plain language. This turns out to be a very important and timely action, since researchers have been increasingly criticized for using blind, mechanistic application of significance testing to provide a patina of scientific legitimacy to fundamentally weak research practices. On Monday, the American Statistical Association (ASA) released a consensus statement to address the misuse of p-values and promote a better understanding of them among researchers. This hits close to home for us in the Sustainable Transportation Lab, as statistical analysis is at the heart of much of our research. 
P point oh oh five, then null is rubbish!” A limerick by Roderick Little highlights the importance of recent events in the statistical community:
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