In a research paper, you need to describe your methods such that other researchers can redo the same research. This is called reproducibility. This way, the validity of your results can be verified. Hence, journals require you to state the formulas used for any unusual or unconventional statistical test.

In contrast, if you have used a popular statistical test (e.g., ANOVA and t-test), researchers in your field probably already know how to perform the test and don’t need to be told how to do it. Therefore, you don’t need to describe the analytical method extensively for commonly used statistical tests.

Hope that helps. For more insights, you may go through these similar queries by other researchers:

• Do I have to report the results for each procedure described in the Methods section?
• Should I write the definition and working of an instrument or scale that I used in my study?
• How do we describe the use of software in the Materials and Methods section of a dissertation?