So would this rephrasing from your example also be correct?
If there truly is no correlation between [Chemical A] and [Condition X], there would be a 1% probability that due to random chance alone, we would see a big enough difference between patients and controls to erroneously suggest there is a correlation. i.e. 1% chance of a false positive.
Kind of. The p-value is derived from the measurements we have already taken. So I would rephrase your rephrasing as:
If there truly is no correlation between [Chemical A] and [Condition X], there would be a 1% probability that due to random chance alone, we would see a difference between patients and controls at least as large as we've measured in our current experiment
Taking a simpler example:
- I have a coin in my pocket that I think is biased towards coming up heads.
- The null hypothesis is that it is fair and has an equal probability of coming up heads or tails.
- I toss the coin six times. It comes up heads five times.
- My p-value is the probability that, if the null hypothesis is correct, I got the result I did - i.e. if the coin is fair, what is the probability of getting at least five heads upon six coin tosses.
Last edited: