February 11, 2021

# Short steps on how to read a paper: Part 12: Probability

In this short step, I hope to explain probability or p values.  I wonder if readers of papers do not always understand the meaning of p-values?  This information is not a complex area of an article. But I wonder if authors and statisticians unintentionally make it complicated.  So here is my attempt at explaining p values.

##### Let’s look at probability.

We all know that if we toss a balanced coin 100 times, there is a fair chance that we will get heads and tails 50 times each.  This means that the probability of heads or tails is 50:50.

P values in a scientific paper represent the chances of a particular result.  In the coin-tossing exercise, we can say that p=0.5.

When we look at a scientific paper, there is always a probability that a difference between interventions has occurred entirely by chance. We, therefore, have to decide on the level of probability we can accept.

Statisticians have decided that the level of risk that we should accept that a result has occurred by chance is 5% or p=0.05. This figure is often called statistical significance.  Therefore, if we are reading a paper and the authors report that the difference is statistically significant at p<0.05, then we are taking a 5% risk that any difference has occurred by chance.

When p<0.01, the risk we are taking is 1%.

It is as simple as that.

##### Now to complicate things!

All this is very well. But what happens if p<0.07. It is not statistically significant. But the risk is still low at 7%. In this case, as readers, it is up to us to decide if this is sufficient risk for us to accept that there is a difference. Therein, lies a big problem with P values- the relatively arbitrary nature of the cut-off. This is why statisticians like to see P values presented with associated effect sizes and confidence intervals. The latter helps us evaluate the size and potential relevance of any difference and the precision of that estimate of effect.

It is also crucial to realise that if a result is p=<0.01, it does not mean that it is any more important than p<0.05.  Authors tend to get excited about low p values.  But they only mean that the probability of a result occurring by chance is lower.

I hope that this explanation is clear, if not, ask in the comments section.

Next week I am going to look at effect size.

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