Most of the time having a p-value below some cut-off value is a good thing, but sometimes good things occur when the value is above the cut-off (see p-values for programmers for details about what the p-value is).
A commonly encountered cut-off value is 0.05 (sometimes written as 5%).
Where did this 0.05 come from? It was first proposed in 1920s by Ronald Fisher. Fisher’s Statistical Methods for Research Workers and later Statistical Tables for Biological, Agricultural, and Medical Research had a huge impact and a p-value cut-off of 0.05 became enshrined as the magic number.
To quote Fisher: “Either there is something in the treatment, or a coincidence has occurred such as does not occur more than once in twenty trials.”
Once in twenty was a reasonable level for an event occurring by chance (rather than as a result of some new fertilizer or drug) in an experiment in biological, agricultural or medical research in 1900s. Is it a reasonable level for chance events in software engineering?
A one in twenty chance of a new technique resulting in a building falling down would not be considered acceptable in civil engineering. In high energy physics a p-value of is used to decide whether a new particle has been discovered (or not).
In business p-values should be treated as part of cost/benefit analysis. How confident are we that this effect is for real, how much would it cost to be right or wrong about it? Using a cut-off value to make yes/no decisions (e.g., 0.049 yes, 0.051 no) is very simplistic decision making.
To get a paper published in a software engineering journal requires any data analysis to have p-values below 0.05. In this regard the editors are aping journals in the social sciences; in fact the high impact social science journals require p-values below 0.01 (the high impact journals receive more submissions and can afford to be choosier about what they publish).
What is a sensible choice for a p-value cur-off in software engineering journals? The simple answer is: As low as possible, given the need to accept papers per month for publication. A more complicated answer would involve different cut-offs for different kinds of measurements, e.g., measuring people or measuring code.
While the p-value attracts plenty of criticism, there is nothing wrong with p-values. Use of p-values has a dominant market position in statistics and they are frequently misused by the clueless and those wanting to mislead their audience. Any other technique is just as likely to be misused, if not more so.
The killer phrase associated with p-values is “statistically significant”, often abbreviated to just “significant”. How people love to describe the results of their measurements as being shown to be “significant”. Of course, I am free to choose whatever p-value cut-off I like for my experiments and then claim the results are significant. I have had researchers repeatedly tell me that their results were “significant”, every time I asked them about p-values; a serious red flag.
When dealing with statistical results, ask yourself what the reported p-values mean to you. Don’t accept the 0.05 is the cut-off that everybody uses nonsense. If the research won’t reveal actual p-values, walk away from the snake oil.