No, the p-value is the probability that the given data generated is as far away or farther by random chance given the null hypothesis is true. That is to say, we assume the null hypothesis to make some predictions and see if the data is a likely occurrence under those assumptions.
This is not the same as the probability that the null hypothesis is true. If that is what you want (and most of us do want this), then Bayesian methods are more appropriate though they are more complicated and more sensitive to initial assumptions.
Sure, but thats why the null hypothesis should be predicted by your theory. Then you are checking your theory. Most people could care less about whether there is a miniscule difference between groups or not.
>"The p-value is the probability that the null hypothesis is true."
No, as pointed out by jostylr this is wrong.
If you start by assuming A and B are related, your experiment would have to fail reject that notion in order to prove that A and B are indeed related, which is a less direct way of approaching scientific discovery.
This usually means that the alternative hypothesis is the ‘interesting’ one, which is probably what the researcher would like to occur. Which maybe isn’t entirely intuitive.
But I f you don’t follow those restrictions, the math is meaningless.
If you swap the terms in the math, you’ll confuse anyone who knows the stats, while not really benefitting anyone.
And if you’re not using the math, why refer to a ‘null’ and ‘alternative’ hypothesis at all?
"Null" stands for hypothesis to be nullified in this case, not zero.
But now let's say that you assume they are different. Well, how different are they? You need to make that choice in order to get predictions. And then your rejection is not a rejection of "being different" but "being different in this one specific way".
Yes, precisely. You should predict a specific thing will happen based on some theory and check it with data. This sounds like the science we learned about in school.
Only predicting "there should be some difference" with your theories is more like astrology or something.
