To add a little more to this post, I’ve read several papers where the authors add some details regarding the statistical methods/tests used with the results rather than just reporting a p-value. I think this approach really adds clarity. Here is an example. First, what I see as a typical approach:
We found that the treatment group performed significantly better than the control group (p=0.01).
We can assume that maybe a two sample t or proportion test was used and was noted in the statistical results section. If we add that minor detail to the sentence, note the improvement.
Using a two independent sample t-test, we found that the treatment group performed significantly better on average than the control group (t=2.5, p=0.01).
I don’t think it’s necessary to add all the details, e.g., were the variances assumed to be equal or not (that level of detail could be included with a supplemental, along with the data and code), but at least noting the test in my opinion makes clear that the correct statistical method was used.