# What is a p-value?

In clinical research, the aim of a study is usually to determine the efficiency of a treatment or an intervention studying the difference of a clinical outcome between two or more groups of patients.

The p-value is the probability of observing a difference of means or proportions between the groups of patients as extreme as the one observed if these hypotheses are true:

- the sample tested has been randomly drawn
- the study has been performed respecting the good practices in methodology for biomedical research
- the mathematical laws which have to be respected for the test performed to be reliable are effectively followed by the data
- the means or proportions between the groups tested are equal

Thus, a p-value only allows to suppose that all these hypotheses are true or that at least one of them is false.

This statistic is usually used to invalidate the hypothesis that the means or proportions of the groups tested are equal: if we ensure that the other hypotheses are true, a p-value lowest than 1 indicates a divergence between this hypothesis and reality. Smaller is the p-value, higher is the confidence researchers suppose they can have in the invalidation of this hypothesis.

How should I interpret a p-value?

The p-value is interpreting using a risk indicator called α. The risk α is the risk of mistaking in concluding that the hypothesis of equality of means or proportions between groups is false. This risk corresponds to the threshold researchers would like to fix for the p-value to conclude that the hypothesis of equality of means or proportions between groups is false.

The threshold usually used in biomedical research is 0.05. In this case, if the p-value is inferior to 0.05, researchers conclude that this hypothesis is false; otherwise, if the p-value is above 0.05, they decide that the study didn't give enough information to know which hypothesis is false (equality of means/proportions, sample not randomly drawn, study protocol to be improved...).

For more details about usual misinterpretations of p-values, you can refer to this article:

Greenland S., Senn S.J., Rothman K.J., Carlin J.B., Poole C., Goodman S.N., Altman D.G. Statistical tests, P values, confidence intervals, and power: a guide to misinterpretations. Eur J Epidemiol. 2016;31:337–350. DOI 10.1007/s10654-016-0149-3.

# Why is it unrecommended to use p-values in the baseline characteristics table in randomized studies?

A p-value in population baseline characteristics table usually doesn't refer to a research question.

The baseline characteristic table aims to describe the characteristics of the groups to validate the comparability of the groups before intervention. But in fact, if this comparability were to be invalidated, it would mean that the study doesn't have a sufficiently high methodology level to make conclusions. Thus, the baseline characteristics description suppose that the groups are effectively comparable, a p-value isn't necessary.

# Where will the p-values be displayed in EasyMedStat?

The use of p-values is needed in all testing situation: the test between means (Welch's test, Mann-Withney's test,...), the test between two proportions (Chi² test, Fisher's test,...), the survival analysis or in multivariate analysis, for instance.

# Is the p-value enough to conclude?

Absolutely no. You should never conclude on the sole p-value of a test.

There are some situations where a p<0.05 does not mean that you can take a clinical conclusion:

- When you have a very large number of patients, your p-values will frequently be below 0.05 just because you have large samples
- When your p-value < 0.05 but the absolute difference between the 2 groups is small, be careful with your conclusions. For example, if the pain level is 3.1 (out of 10) in group A and 3.2 (out of 10) in group B, would you consider that group A had better treatment than B? Not necessarily.
- When you give the result of a test, always provide the confidence interval of the difference or of the odds-ratio. This gives additional data to your readers.

The American Statistical Association published a statement about p-values that you can find at this URL: https://www.amstat.org/asa/files/pdfs/p-valuestatement.pdf It is worth reading.