In general, p values tell readers only whether any difference between groups, relationship, etc., is likely to be due to chance or to the variable(s) you are studying. According to most statistical guidelines, including those provided by Nature, you need to provide a p value for any change, difference, or relationship called “significant.” Further, because the significance threshold (i.e., the p value that you use as a cutoff for determining significance) can be .05, .001, or .01, it’s advisable to state the significance threshold used in your research in the Methods section of your paper. A sentence like “The significance threshold was set at .05” is all that is required.

However, a p value cannot tell readers the strength or size of an effect, change, or relationship. Therefore, you should avoid reporting nothing else but p values. It’s always a good idea to provide a test statistic (t, F, U, etc.), correlation or regression coefficient (Pearson’s r, Spearman’s rho, etc.), or measure of effect size (eta-squared, partial-eta-squared, omega-squared, etc.).

Let’s take the example of the sentence “We found a significant relationship between anxiety and job satisfaction (p < .05).” Here, all you are telling the readers is that you have enough evidence that this relationship is unlikely to be due to chance. Readers don’t know whether this relationship is direct or inverse (i.e., did participants with higher anxiety have higher job satisfaction or did participants with lower anxiety have higher job satisfaction?). Further, was this relationship strong or weak? For the benefit of the reader, you should also report a correlation coefficient along with the p value. If you add “r = -.78” in the parentheses at the end of the above sentence, your readers will understand that this is a strong inverse relationship. Thus, they get a better idea of your actual findings.

Here’s another example: “We found a significant difference between pretest and posttest scores.” I would recommend reporting (a) the test statistic so that the reader knows what statistical test you performed to examine this difference and (b) a measure of effect size so that the reader understands how large this difference is. Even the mean pretest and posttest scores could be sufficient for readers to understand the size of the effect you have found.

In addition, it’s a good idea to report exact p values, since this practice makes for greater scientific integrity. In the above sentence, the p value could be “.048”; this value is technically below “.05” but so close to .05 that it would probably need to be treated like a p value of .51, which is not statistically significant. Typically, if the exact p value is less than .001, you can merely state “p < .001.” Otherwise, report exact p values, especially for primary outcomes. 

Furthermore, here are a couple of basic errors I’ve come across with regard to p values:

1. “p =  .00” or “p < .00”

Technically,  p values cannot equal 0. Some statistical programs do give you p values of .000 in their output, but this is likely due to automatic rounding off or truncation to a preset number of digits after the decimal point. So, consider replacing "p = .000" with "p < .001," since the latter is considered more acceptable and does not substantially alter the importance of the p value reported. And p always lies between 0 and 1; it can never be negative.

2. “p < .03”

Many journals accept p values that are expressed in relational terms with the alpha value (the statistical significance threshold), that is, “p < .05,” “p < .01,” or “p < .001.” They can also be expressed in absolute values, for example, “p = .03” or “p = .008.” However, pvalues are conventionally not used with the greater than (>) or less than (<) sign when what follows the sign is not the alpha value.

One last tip: Many authorities in scientific, technical, and medical fields recommend that a zero should not be inserted before a decimal fraction when the number cannot be greater than 1 (e.g., correlations, proportions, and levels of statistical significance); that is, “p < 0.05” should be written as “p < .05.”

Do write in a comment with any further questions you may have.