It doesn't. But when you don't have a function for it, you need to test whether there is anything apart from noise. That's the purpose of testing whether we should reject null hypothesis (that all there is, is just white noise).
You start with:
1. ok, this is normal distribution, no function, nothing, just random temperature. Oops, this is so for p-value of 0.5. 2. ok, here is a function that removes solar cycles, now the rest is white noise. Oops, the remainder is white noise for p-value of 0.2 3. ok, here is a function that removes (some other cycle), now the rest is white noise. Oops, the remainder is white noise for p-value of 0.15. 4. ... 5. ok, here is a linear trend of 0.8 C per century, and 0.2 C in the last decade, which removes ever speeding up global warming, now the rest is white noise. Oops, ...what p-value do we get?
(ermmm.... well, I don't do this stuff for living, so I am allowed to make imprecise statements like above. In reality you'd need to turn them "inside out" - because p-value means "if we reject the hypothesis that so and so is white noise, what's the probability of making a mistake", so as we get more and more accurate theories, p-value should be increasing to indicate that what we get is closer and closer to white noise)
no subject
It doesn't. But when you don't have a function for it, you need to test whether there is anything apart from noise. That's the purpose of testing whether we should reject null hypothesis (that all there is, is just white noise).
You start with:
1. ok, this is normal distribution, no function, nothing, just random temperature. Oops, this is so for p-value of 0.5.
2. ok, here is a function that removes solar cycles, now the rest is white noise. Oops, the remainder is white noise for p-value of 0.2
3. ok, here is a function that removes (some other cycle), now the rest is white noise. Oops, the remainder is white noise for p-value of 0.15.
4. ...
5. ok, here is a linear trend of 0.8 C per century, and 0.2 C in the last decade, which removes ever speeding up global warming, now the rest is white noise. Oops, ...what p-value do we get?
(ermmm.... well, I don't do this stuff for living, so I am allowed to make imprecise statements like above. In reality you'd need to turn them "inside out" - because p-value means "if we reject the hypothesis that so and so is white noise, what's the probability of making a mistake", so as we get more and more accurate theories, p-value should be increasing to indicate that what we get is closer and closer to white noise)