How to report P-values

You will routinely find P-values in the output of statistical software.  How should they be reported?

An example

If you’ve suffered from motion sickness, you might have taken a medication (such as “Kwells”) based hyoscine hydrobromide.

In the early 20th century, the effect of hyoscine hydrobromide on sleep was investigated. In his original paper deriving the t-distribution, Student illustrated his methods using data from a study looking at the gain in hours of sleep after using various forms of hyoscine hydrobromide.  Here is a dotplot of the hours gained when the patients used a particular form – Laevo-hyoscine hydrobromide.  The measurement is the hours gained – the difference between using Laevo-hyoscine hydrobromide and not using it.

Here we consider carrying out a single sample t-test of the null hypothesis that the true mean hours gained was zero.

Some output

Here are the results from various software pages.




How you might see the results reported, none of which are recommended

  • P = 0.0050706
    • Too many decimal places!
  • 0.005 in a table labelled “Sig.”
    • It’s the P-value, not “Sig.”
  • P < 0.05
    • That’s only the ball park – the value in relation to an arbitrary threshold.
  • Using the “star” system, and indicating that the result is less by 0.01 by using **.
    • Again, that’s only the ball park.
  • Stating that the result is statistically significant. 
    • That’s the implied ball park!  That only has implied numerical meaning.

 How to report P-values

  • If you are reporting P-values in an academic paper or thesis, it’s good practice to report the actual value to three decimal places.
  • If the P-value is very small, common practice is to report it as < 0.001.
  • It’s not sufficient to only report a P-value; relevant estimates and confidence intervals should also be provided.

For example, patients gained an average of 2.3 hours of sleep when using Laevo-hyoscine hydrobromide, with a 95% confidence interval of 0.9 to 3.8 hours. The P-value for a test of the null hypothesis that the true average gain was zero hours was P = 0.005.

Student’s paper

Student (1908) The probable error of the mean. Biometrika, 6, 1-25.