In a broad sense, plausibility is usually used as another name for “reasonable.” Let’s say you wanted to check a normal model, obtained from a sample, to see if it is a reasonable model for the population. An effective way to check the assumption that a normal model is plausible is to create a normal probability plot from the sample data (Johnson, 2009).
Various statistics can also be plausible, in the “reasonable” sense of the word. For example, you could say that a point estimate is a plausible value for a parameter: it isn’t exact, but it’s a reasonable estimate.
Depending on the author though, “plausibility” could also mean “probability.” For example, the “plausible” in following statement about hypothesis testing could easily be switched out for the word “probable”:
“If the probability is large then the null is plausible and we cannot reject the null hypothesis” ~ (Rao, n.d.)
Similarly, the same could be said about “plausible values” here being swapped for “probable values”:
“On the other hand, if we report a range of plausible values – a confidence interval – we have a good shot at capturing the parameter.” ~ (Libretexts)
The two words have been confused for many centuries, and the failure of what Ramirez and Selin (2013) call “… unsatisfactory and unproductive distinctions” between the two terms is one reason why it’s very hard to pin down a catch-all definition. To muddle the situation even further, plausible and likelihood are often used synonymously.
The takeaway? Use caution when reading any article that mentions plausibility, to be sure of the specific author’s intent.
Plausibility Measure
While “plausibility” is an oft-confused term, plausibility measure is relatively well defined. A plausibility measure is an approach to measuring uncertainty—an element in partially ordered space. The term does have surprisingly little structure, as just about every approach to calculating statistical uncertainty can be called a plausibility measure (Friedman & Halpern, 2013).
References
Friedman, N. & Halpern, J. (2013). Plausibility Measures: A User’s Guide. Retrieved February 3, 2020 from: https://www.cs.cornell.edu/home/halpern/papers/plausibility_manual.pdf
Johnson, R. (2009). Statistics: Principles and Methods. John Wiley & Sons.
Libretexts. Confidence Intervals.
Ramirez, R. & Selin, C. (2013). Plausibility and Probability in Scenario Planning. Retrieved February 3, 2020 from: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.982.6035&rep=rep1&type=pdf
Rao, S. (n.d.). Understanding Hypothesis Tests.