# 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.

### R

### Minitab

### SPSS

### 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.”

- It’s the
*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*P*< 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.