Methods: P values

JAMA is running a guide to statistics and methods series. I come across methods tutorials in other journals from time to time as well. I think I’ll start excerpting and pointing readers to them.

Let’s start with P values, as discussed recently in The BMJ. The setting is an examination of birth weight of infants whose mothers had been randomized to receipt of a certain diet (low glycemic index, but that doesn’t matter) or not.

The P value for the statistical test of birth weight was P=0.449. The P value represents the proportion of the theoretical infinite number of samples—that is, 0.449 [44.9%]—that have a mean difference in birth weight equal to, or greater than, that observed in the trial above. This is irrespective of whether the mean birth weight was higher or lower for the intervention group than for the control group. More formally, the P value is the probability of obtaining the observed difference between treatment groups in mean birth weight (or a larger one), irrespective of the direction, if there was no difference between treatment groups in mean birth weight in the population, as specified by the null hypothesis. The P value for the statistical test of the primary outcome of birth weight was P=0.449, which was larger than the critical level of significance (0.05). Hence there was no evidence to reject the null hypothesis in favour of the alternative. The inference is that there was no evidence that the intervention and control treatments differed in mean birth weight in the population.

Usually when I read a P value (or any statistic), I try to get my mind to interpret it according to the definition. I try not to let my mind wander into other (false) characterizations. For instance, I would read P=0.449 as, “Assuming the null hypothesis to be true (i.e., no effect of the diet), the probability of obtaining at least the observed weight difference between diet and control groups is 0.449.” (Secret: Because of the wishy-washy language in most papers, I’m often confused by the reporting of hypothesis tests and the only reliable way I’ve found to understand them is to go back to the definition.)

I could write a lot more here, and I nearly did. But I’m going to try to keep these methods posts very short and focused. So, I’ll stop. Read The BMJ paper for more on P values, though you can find information elsewhere I’m sure. Also, I’m opening up comments to discuss P values and to solicit pointers to other good, simple methods papers. Feel free to provide additional resources. (Comments automatically close one week from the post’s time stamp.)

@afrakt