I have actually been studying and using statistics a lot in my career, but I still struggle with finding a simply way to explain what exactly is p-value.
In: Mathematics
When you test or experiment on something the idea is very typically to have 2 complementary assertions (or hypothesis). Say you’re trying to discover if factor X has any effect on outcome Y.
Null hypothesis: X has no impact on outcome Y
Alternative hypothesis: X has an impact on outcome Y
Experiments or samples are taken to determine which of these are likelier to be true – and this experiment results in outcome Z. To be conservative, we start by ASSUMING that the null hypothesis holds or is true. The p-value measures “how likely am I to achieve an experimental outcome Z assuming the null hypothesis is true”.
A low p-value means that outcome Z is less likely to occur if the null hypothesis is true. In other words a low p-value gives credence to the idea that the alternative hypothesis is more explanatory of outcome Z.
Say you’re flipping a particular coin, you think the coin is not a fair coin. An experiment is conducted where the coin is flipped 1000 times. The null hypothesis is “the coin is fair” and the alternative is that “the coin is unfair”.
If the outcome is that there were 501 heads and 499 tails, you will get a p-value that is pretty high. This means that this particular outcome is rather likely if the coin is fair. If the outcome is that there were 700 heads and 300 tails, you will get a very low p-value. This indicates that the null hypothesis is less likely to be true and the alternative hypothesis “the coin is unfair” is likelier to be true.
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